I know people have tried to give a stringy description of pure
YangMills theory, and this has been worked out in great detail
for 2d YM theory, but remains mysterious in higher dimensions.
To the extent that it works at all, it requires a different action
than the usual Polyakov action.
But, most of this work is on nonabelian YangMills theory!
You'd think the comparatively trivial abelian case would be a
lot easier: either it should definitely work, or definitely not work.
> Here's a rather perversesounding question: has anyone figured
> out a way to give a stringy description of the usual quantized
> vacuum Maxwell equations on flat spacetime?
Yes, U(1) gauge fields are a part of a large fraction of the stringy
backgrounds that people study. U(1) gauge field is what lives on a single
Dbrane. U(1) gauge fields is what one gets by a dimensional reduction
from a compactification on circle  from the metric g_{d,mu} via the
KaluzaKlein mechanism, or from the Bfield that couples to the strings
themselves. U(1) gauge fields are often remainders of a larger, broken
nonAbelian symmetry.
> No matter, no supersymmetry, no gravity... just photons?
Nope. String theory *predicts* the existence of gravity, and more or less
the existence of supersymmetry. (I am talking about the "full" string
theory, as opposed to various decoupled limits that may contain no
gravity, or at least no obvious gravity.)
String theory does not belong to the class of the "theories" where you can
freely decide what spectrum and physics you want to have in your spacetime
(and perhaps even what are the answers to all other questions), and then
you try to prove that it is possible (that there exists a "representation"
of your assumptions). String theory is a *predictive* theory. It predicts
gravity; under certain assumptions, it also predicts supersymmetry (that
can be broken). It tells us what is possible and what is not possible. It
is also very difficult to study nonsupersymmetric backgrounds because
supersymmetry is otherwise useful to guarantee various cancellations that
stabilize the background and simplify our calculations.
The spectrum of possible string theories is constrained a lot. For
example, if you look at 10dimensional supersymmetric theories, you can
see from low energy field theory that type IIA, type IIB, type I with E8 x
E8 and type I with SO(32) supergravities (plus super YangMills in the
two latter cases) are the only anomalyfree choices. Miraculously, there
exists a stringy completion for each of them (the last choice has two
stringy completions that are Sdual to one another, and some of them
have an 11dimensional interpretation).
You can be sure that there is no U(1) YangMills coupled to supergravity
in 10 dimensions that would be consistent  although an allowed choice is
U(1)^496 or U(1)^248 x E8, and therefore there is no string theory that
would describe this (nonexistent) background with one U(1) only. It will
probably sound a too trivial sentence for many readers, but I should
emphasize that string theory is *not* the same thing as Maxwell's theory.
It is also not a collection of theories that are identical to Maxwell's
theory and similar ones. String theory always predicts new physics, a very
specific pattern of new physics.
> I know people have tried to give a stringy description of pure
> YangMills theory, and this has been worked out in great detail
> for 2d YM theory, but remains mysterious in higher dimensions.
> To the extent that it works at all, it requires a different action
> than the usual Polyakov action.
There is only one string theory. The purpose of string theory is not to
give a "description" (or justification) of an arbitrary system of fields
that you invented independently. The purpose of string theory is to
predict what physics, fields, and interactions actually exist, what the
cross sections, entropies and spectra actually are, and most choices are
impossible.
If you talk about a theory that is not based on the Polyakov action or
something connected to it by physical operations or gaugefixing, I don't
know why you think that it should be called "string theory". A random
manipulation with some random twodimensional theories certainly cannot be
called "string theory".
> But, most of this work is on nonabelian YangMills theory!
> You'd think the comparatively trivial abelian case would be a
> lot easier: either it should definitely work, or definitely not work.
Should not you just ask the question whether a U(1) theory with (or
without) something else is a solution of string theory? If you said
"without gravity", then the answer would be "no". The number of
backgrounds  allowed "classical" solutions  in string theory is large,
but it is certainly not unconstrained. ;)
______________________________________________________________________________
Email: lu...@matfyz.cz fax: +1617/4960110 Web: http://lumo.matfyz.cz/
eFax: +1801/4541858 work: +1617/4968199 home: +1617/8684487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Only two things are infinite, the Universe and human stupidity,
and I'm not sure about the former.  Albert Einstein
>String theory *predicts* the existence of gravity, and more or less
> the existence of supersymmetry. (I am talking about the "full" string
> theory, as opposed to various decoupled limits that may contain no
> gravity, or at least no obvious gravity.)
On the other hand, it seems like virtually every field theory that one can
write down can be understood as describing some string theory configuration
in the low energy and alpha' >0 limit. In many cases finding the stringy
physics that a certain field theory comes from in some limit helps to
understand that field theory.
There is a recent nice example hepth/0402160, where it is shown how N=1/2
susy U(N) gauge theories in D=4 can be nicely understood by means of Type II
on CY with D3 branes and constant RR 'graviphoton' background.
Maybe all that John Baez is asking for is something like the lowenergy
limit of a single
( i.e. U(N=1) ) D3 brane (maybe in some orbifold to make things work) for
the bosonic string. I bet that if he tells us what exactly he wants to know
from a stringy generalization of U(1) YM somebody will be able to provide
something appropriate.
> On the other hand, it seems like virtually every field theory that one can
> write down can be understood as describing some string theory ...
Assuming that you decouple gravity, it is the case, and there is a whole
industry of "geometric engineering" whose purpose is to construct the
geometric background for string theory with the desired low energy limit.
> There is a recent nice example hepth/0402160, where it is shown how N=1/2
> susy U(N) gauge theories in D=4 can be nicely understood by means of Type II
> on CY with D3 branes and constant RR 'graviphoton' background.
Interesting! I missed this one.
> Maybe all that John Baez is asking for is something like the
> lowenergy limit of a single ( i.e. U(N=1) ) D3 brane (maybe in some
> orbifold to make things work)
The first pages of Chapter 13 of Polchinski, or some corresponding section
in the first volume? I don't know precisely what he wants to see. A paper
containing the sentence "this system leads to U(1) gauge theory at low
energies", with an equation expressing the Maxwell action? ;) That would
not be a terribly intelligent paper, unless it was the first paper on
Dbranes. :)
D3branes in bosonic string theory contain not only the YangMills field,
but also the 22 transverse scalars, and the lowenergy physics is that of
a DiracBornInfeld action. If you want theories without any transverse
scalars etc., you should rather make some sort of compactification, but at
any rate, the heavily nonsupersymmetric backgrounds will always be
dangerous because the quantum corrections won't be under control.
>
> On 8 Mar 2004, Urs Schreiber wrote:
>
> > On the other hand, it seems like virtually every field theory that one can
> > write down can be understood as describing some string theory ...
>
> Assuming that you decouple gravity, it is the case, and there is a whole
> industry of "geometric engineering" whose purpose is to construct the
> geometric background for string theory with the desired low energy limit.
Can you give some recommended referances for this sortof work? I haven't
had much luck finding papers in which low energy effective field theories
have been calculated.
>"Lubos Motl" <mo...@feynman.harvard.edu> schrieb im Newsbeitrag
>news:Pine.LNX.4.31.040308...@einstein.physics.harvard.edu...
>> String theory *predicts* the existence of gravity, and more or less
>> the existence of supersymmetry. (I am talking about the "full" string
>> theory, as opposed to various decoupled limits that may contain no
>> gravity, or at least no obvious gravity.)
Yeah, yeah  I know all that stuff.
>On the other hand, it seems like virtually every field theory that one can
>write down can be understood as describing some string theory configuration
>in the low energy and alpha' >0 limit. In many cases finding the stringy
>physics that a certain field theory comes from in some limit helps to
>understand that field theory.
Right, this is the sort of thing I was talking about.
I want to get just photons on Minkowski spacetime  nothing else.
I allow you to start with string theory on any sort of background you want,
and take any sort of limit you want, or play any other sort of trick
you know. You can start with bosonic string theory if that helps.
You can even start with a nonstandard string action if you want.
>Maybe all that John Baez is asking for is something like the lowenergy
>limit of a single ( i.e. U(N=1) ) D3 brane (maybe in some orbifold to make
>things work) for the bosonic string.
I'm not too fussy. If it does what I ask for above, I'll be interested.
>I bet that if he tells us what exactly he wants to know
>from a stringy generalization of U(1) YM somebody will be able to provide
>something appropriate.
It's not like I have some hard question about the quantized vacuum
Maxwell equations and I want to use string theory to answer it!
I just want to "see the theory in terms of strings" somehow, and see
what it would look like that way. And, I really *DON'T* want photons
coupled to lots of matter fields and gravity. If they are, I'd like
to tune parameters in some way that makes these couplings negligible 
i.e., consider some limit where they go away.
> > There is a recent nice example hepth/0402160, where it is shown how
N=1/2
> > susy U(N) gauge theories in D=4 can be nicely understood by means of
Type II
> > on CY with D3 branes and constant RR 'graviphoton' background.
>
> Interesting! I missed this one.
As soon as I find the time I would like to discuss that paper in more
detail. A first couple of comments are at
http://golem.ph.utexas.edu/string/archives/000323.html .
> > Maybe all that John Baez is asking for is something like the
> > lowenergy limit of a single ( i.e. U(N=1) ) D3 brane (maybe in some
> > orbifold to make things work)
>
> The first pages of Chapter 13 of Polchinski, or some corresponding section
> in the first volume?
Perhaps. Maybe equation (13.3.34) would already help? Or section 7.4 of the
lecture notes hepth/0207142?
Open strings on branes give gauge theories on these branes and it seems like
any conceivable gauge theory can be understood as the lowenergy limit of
some Dbrane system. As far as my very incomplete understanding goes this is
deeply connected to string/gauge duality. Given any field theory you are
really looking at the lowenergy limit of strings on some branes.
Let's see what has been done in the literature that might help regarding
Maxwell theory, i.e. U(1) YM, from the string point of view. How about
Yosuke Imamura, A D2brane realization of MaxwellChernSimonsHiggs
systems,
hepth/0012254
Abstract:
We show that N=2 supersymmetric MaxwellChernSimonsHiggs systems in three
dimension can be realized as gauge theories on a D2brane in D8branes
background with a nonzero Bfield. We reproduce a potential of Coulomb
branch of the ChernSimons theory as a potential of a D2brane in a
classical D8brane solution and show that each Coulomb vacuum is realized by
a D2brane stabilized in the bulk at a certain distance from D8branes.
?
> Can you give some recommended referances for this sortof work? I haven't
> had much luck finding papers in which low energy effective field theories
> have been calculated.
If you ask about geometric engineering, you can start, for example, with
the papers that have "geometric engineering" in the title. Be ready for a
rather difficult geometry. See
http://wwwspires.slac.stanford.edu/spires/find/hep/www?rawcmd=find+title+geometric+engineering
http://wwwspires.slac.stan
ford.edu/spires/find/hep/www?rawcmd=find+title+geometric+engineering
I included the URL twice, so that if the first copy does not work, you can
get the full URL by combining the last two lines.
______________________________________________________________________________
Email: lu...@matfyz.cz fax: +1617/4960110 Web: http://lumo.matfyz.cz/
eFax: +1801/4541858 work: +1617/4968199 home: +1617/8684487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
To be more specific, you just want a metric, a bivector, and a tangent
space in which
Fmn,n = 0
right?
Sounds easy enough!
drl
> >Maybe all that John Baez is asking for is something like the lowenergy
> >limit of a single ( i.e. U(N=1) ) D3 brane (maybe in some orbifold to
make
> >things work) for the bosonic string.
>
> I'm not too fussy. If it does what I ask for above, I'll be interested.
Yes, the low energy effective worldsheet theory of a single flat D3 brane of
the bosonic string is, to lowest nontrivial order, just U(1) gauge theory in
4D with nothing else.
On Tue, 9 Mar 2004, John Baez wrote:
> Right, this is the sort of thing I was talking about.
> I want to get just photons on Minkowski spacetime  nothing else.
I thought that you said that you understood that string theory always
contains gravity, so how can you only want photons on Minkowski spacetime?
Of course that one can take various limits to get rid of everything and
study the decoupled free photons only, but what can such a procedure ever
be good for? Free Maxwell's field is a trivial theory. We only study
various gauge theories embedded to string theory because string theory
allows us to geometrize many questions and give them answers that were
hard or impossible before; U(1) free theory does not have any interesting
geometry associated with it. String theory is a *scientific* theory, so
its purpose is to *derive* answers to various questions  answers that are
not known a priori.
Your approach  and in fact the approach of current algebraic quantum
field theory and loop quantum gravity alike  is different. You first
decide what the answers should be, probably because you think that all
answers to all questions have already be found and showed to you by a
divine force, and then you're looking for a "scientific" theory that
confirms all these answers. I don't think that this is a scientific
approach, and it is extremely unlikely that such an approach would ever
lead to some interesting developments or even to the truth.
String theory is a *scientific* theory, and it's only meaningful because
it gives answers that were not clear a priori.
> I allow you to start with string theory on any sort of background you want,
> and take any sort of limit you want, or play any other sort of trick
> you know. You can start with bosonic string theory if that helps.
> You can even start with a nonstandard string action if you want.
String theory does not really have "standard" and "nonstandard" actions
that would give different results. A physical picture or calculation in
string theory is either *correct*, or *wrong*. There is no room for fuzzy
questions of this sort in string theory.
> It's not like I have some hard question about the quantized vacuum
> Maxwell equations and I want to use string theory to answer it!
This is exactly why I say that your question is not a scientific one. Why
do you ask questions if you realize that you don't really have any "hard"
questions that you want to be answered?
> I just want to "see the theory in terms of strings" somehow, and see
> what it would look like that way. And, I really *DON'T* want photons
> coupled to lots of matter fields and gravity. If they are, I'd like
> to tune parameters in some way that makes these couplings negligible 
> i.e., consider some limit where they go away.
On paper, you can tune the string coupling constant to zero which turns of
*all* interactions. Then you can think of all particles separately because
they are decoupled. I don't need to do anything fancy to get a free U(1)
gauge theory. The limit g=0 of *any* theory that contains such particles
allows us to decouple the photons from everything else (and all other
particles are also decoupled from one another). This g=0 point is a
singular point in the moduli space; it really does not belong to the
moduli space, and it is only interesting as a zeroth approximation to
study the full interacting theory at regular points of the moduli space.
Perturbative string theory on a simple background (e.g. in the infinite
Minkowski space of the critical dimension) only has one coupling constant
that can be tuned, everything else is determined. Once supersymmetry is
broken (in a background of a generic enough type), a potential is
generated for all scalar fields and there is *nothing* to finetune. It is
really various *discrete* choices that one can do in string theory to get
various backgrounds, plus *moduli* that allow you to change various things
continuously, but the moduli generically only exist if they're protected
by a certain amount of supersymmetry.
Where's a good derivation of this? I've only seen rather handwaving
arguments as to why this should be true.
Unfortunately, there are a bunch of scalars describing the transverse
fluctuations of the brane.
Aaron
> The first pages of Chapter 13 of Polchinski, or some corresponding section
> in the first volume? I don't know precisely what he wants to see. A paper
> containing the sentence "this system leads to U(1) gauge theory at low
> energies", with an equation expressing the Maxwell action? ;) That would
> not be a terribly intelligent paper, unless it was the first paper on
> Dbranes. :)
>
How accurately can you compute the electron's anomalous magnetic moment
from string theory? To ten decimal places? Exactly? If there such a
calculation in Polchinski's book, I must have missed it.
> Unfortunately, there are a bunch of scalars describing the transverse
> fluctuations of the brane.
I guess that's why you have to put the brane at the singularity of an
orbifold if you want to get rid of the scalars, right?
> >Maybe all that John Baez is asking for is something like the lowenergy
> >limit of a single ( i.e. U(N=1) ) D3 brane (maybe in some orbifold to
make
> >things work) for the bosonic string.
>
> I'm not too fussy. If it does what I ask for above, I'll be interested.
Yes, the low energy effective worldsheet theory of a single flat D3 brane of
Also,
Polchinski, in his book String Theory v. 1,
in Chapter 8 says,
with respect to Dbranes:
"... a flat hyperplane ... a certain open string state
corresponds to fluctuation of its shape. ...
Thus the hyperplane is indeed a dynamical object,
a ... Dbrane ...
When no Dbranes coincide
there is just one massless vector on each,
giving the gauge group U(1)^n in all.
If r Dbranes coincide,
there are new massless states because string that are stretched
between these branes can have vanishing length: ...
Thus,
there are r^2 vectors, forming the adjoint of a U(r) gauge group. ...".
Does that mean that, if as Urs says:
"...a single flat D3 brane ..." gives "... U(1) gauge theory ..."
then
would 2 intersecting/coinciding D3 branes give U(2) gauge theory
and 3 intersecting/coinciding D3 branes give U(3) gauge theory
and 4 intersecting/coinciding D3 branes give U(4) gauge theory
.. etc ... ???
i.e.,
Could you construct the Standard Model from D3 branes in
bosonic string theory, letting up to 3 branes intersect:
U(1) for photons
U(2) for weak bosons
U(3) for gluons
???
Could the U(4) be a compact version of the U(2,2) Conformal Group
that can give gravity by the MacDowellMansouri mechanism,
as described by Mohapatra in section 14.6 of his book
Unification and Supersymmetry, 2nd edition ???
Could the U(5) be related to GUT physics ???
Is there a physical reason to cut off the number of intersecting
D3 branes at 3 or 4 or 5 ????
If you stop at the level of no more than 3 of the D3 branes intersecting,
then would you get a unification of
the standard model from the U(1), U(2), and U(3)
with
gravity, because, as Lubos Motl said,
"... string theory always contains gravity ..." ???
Are there any papers that discuss such a possible development
of (nonsuper) bosonic string theory ???
Tony Smith
web site at http://www.innerx.net/personal/tsmith/TShome.html
According to the old string theory popularization, everything was just
a string only vibrating differently. (As far as I remember, it was
always a closed string, not an open one.) So a little circle doing
the waltz was a photon, but if it was doing a hula it was an electron,
or if a foxtrot, then it was an up quark. (Big Smiley) Something like
that anyway. I never could get an honest answer as to what vibrations
anything like a photon or an electron was doing or what the essential
difference between the two was.
(Of course, I can remember before that when an electron was considered
to be a "point particle".)
Now we have had yet another string revolution, so we have branes as
well as strings. Does your answer mean I should think of a photon as
a D3 brane dancing around, instead of a string?
As you can tell, I do not understand any of this at a technical level.
But I will press on just a little further regardless.
(By the way does U(1) include only the photon and not the electron?
I think this is what John asked for, although it sounds crazy to me.)
What is necessary to include the electron, the photon and the
positron, but not the muon or the proton?
I'll stop there and let you try to deal with a little bit at a time,
if you're willing to do so.
But what I really would like to know is what an uptodate string
theorist now thinks a photon and an electron "look like".
Perhaps you and Lubos could take a crack at this.
TIA.
Jim Graber
> Unfortunately, there are a bunch of scalars describing the transverse
> fluctuations of the brane.
Depending on John Baez's intended application, if the number of dimensions
is not an issue the simplest thing probably would be to consider the single
spacefilling D25 brane of the bosonic string. This one does not have any
transverse fluctuations and there is indeed only the U(1) gauge field.
> Unfortunately, there are a bunch of scalars describing the transverse
> fluctuations of the brane.
Depending on John Baez's intended application, if the number of dimensions
> According to the old string theory popularization, everything was just
> a string only vibrating differently. (As far as I remember, it was
> always a closed string, not an open one.)
Closed strings give gravity, open strings give gauge fields (modulo
subtleties, see below).
More precisely, the massless spectrum of closed strings contains
NSNS sector:
 the graviton
 the dilaton
 the quantum of the KalbRamond field
NSR sector:
 the gravitino
 the dilatino
RR sector:
 quanta of pform fields
while that of open strings contains:
NS sector:
 the gauge boson
R sector:
 spinors .
(R sector means that worldsheet fermions are periodic, NS sector means that
worldsheet fermions are antiperiodic)
All these massless states are ground states with respect to the worldsheet
theory, i.e. in these states the string vibrates as little as is admissable
by the rules of quantum mechanics.
> So a little circle doing the waltz was a photon,
This depends on where you get the U(1) gauge group form.
It might come by the KaluzaKlein mechanism from a column of the metric
tensor. In this case the photon would indeed be a state of the closed
string, namely that where one half of the oscillators on the worldsheet is
polarized along the compact direction while the other half carries an index
in the observable dimensions.
You can also get U(1) from the open string sector, because the open string
generally has the gauge bosons (because due to the boundary conditions there
is only one set of worldsheet oscillators and hence only a single spacetime
index).
If you are looking for a visualization for the "waltz of a photon" in the
latter sense try this:
http://groups.google.de/groups?selm=3E973BB4.273CFACD%40uniessen.de
For the bosonic string visualization of the massless states is easy: The
massless states of the open bosonic string look like periodically expanding
and contracting open rubber bands, where the direction of expansion is the
direction of polarization. The graviton, dilaton KalbRamond states of the
closed bosonic string would look something like superpositions of Lissajou
figures, I think.
For the superstring you have to replace the bosonic worldsheet oscillators
in these visializations with fermionic ones. A proposed visualization of
these is given at the above link.
> Now we have had yet another string revolution, so we have branes as
> well as strings. Does your answer mean I should think of a photon as
> a D3 brane dancing around, instead of a string?
No. In the context of branes the photon is a state of an open string which
is attached to the brane. The oscillations of that open string in directions
parallel to the brane give photons (gauge bosons) of the U(1) (U(N)) field
on the brane (the N branes). The transverse oscillations describe
fluctuations of the brane in the ambient spacetime.
> (By the way does U(1) include only the photon and not the electron?
> I think this is what John asked for, although it sounds crazy to me.)
John Baez asked for the photon and just the photon. That's why I offered a
bosonic string on a brane. To get spacetime fermions you need to pick a
superstring.
Unfortunately, there's a tadpole in that configuration. You need 8192
D25 branes to cancel it.
Many thanks for pointing this out. This is making progress towards answering
John Baez' question.
But actually, I am not sure that I understand the significance of this
cancellation. On p. 229 of Polchinski it says
"the tadpole is proportional to 2^13 \mp N. For the gauge group SO(2^13) =
SO(8192) this vanishes, the tadpoles from the disk and the projective plane
cancelling. For the bosonic string this probably has no special significance
[...]".
Maybe it depends on what John Baez wants to know from the D25 brane system
whether this is a problem or not?
Anyway, what about the D3 brane on an orbifold singularity? At least for the
superstring I learn from hepth/0402160 that N D3 branes on the singularity
of R^6(Z_2 x Z_2) give U(N) SYM with one supersymmetry on the 4d
worldvolume. I'd guess that by exchanging the superstring for the bosonic
string here we'd get U(N) YM without the superpartners. But I don't claim
that I really understand this sufficiently.
>On Tue, 9 Mar 2004, John Baez wrote:
>> Right, this is the sort of thing I was talking about.
>> I want to get just photons on Minkowski spacetime  nothing else.
>I thought that you said that you understood that string theory always
>contains gravity, so how can you only want photons on Minkowski spacetime?
Because, as you admit:
>[...] one can take various limits to get rid of everything and
>study the decoupled free photons only [...]
and I was interested in seeing precisely which such limits result in
the quantized vacuum Maxwell equations  preferably in 4 dimensions,
but I'm not terribly fussy.
>Free Maxwell's field is a trivial theory.
Right. That should make this limit of string theory particularly easy
to understand in detail, but as Urs and Aaron have pointed out, there
are a few subtleties even here.
>Your approach  and in fact the approach of current algebraic quantum
>field theory and loop quantum gravity alike  is different. You first
>decide what the answers should be, probably because you think that all
>answers to all questions have already be found and showed to you by a
>divine force, and then you're looking for a "scientific" theory that
>confirms all these answers. I don't think that this is a scientific
>approach, and it is extremely unlikely that such an approach would ever
>lead to some interesting developments or even to the truth.
Ho hum. Attacks of this sort are far less interesting than an actual
answer to my question. I'd have hoped you would enjoy what should be
a cute little exercise for an expert in string theory. There's no need
to get so hot under the collar.
> would 2 intersecting/coinciding D3 branes give U(2) gauge theory
>
> and 3 intersecting/coinciding D3 branes give U(3) gauge theory
>
> and 4 intersecting/coinciding D3 branes give U(4) gauge theory
>
> .. etc ... ???
Yes. (modulo subtleties :)
>
> i.e.,
> Could you construct the Standard Model from D3 branes in
> bosonic string theory, letting up to 3 branes intersect:
> U(1) for photons
> U(2) for weak bosons
> U(3) for gluons
> ???
You can indeed construct systems very close to the standard model by
appropriately intersecting D branes. There is an entire industry concerned
with such models. I think the latest review is
D. Luest, Intersecting Brane Worlds  A path to the standard model?,
hepth/0401156
http://arxiv.org/abs/hepth/0401156
> Are there any papers that discuss such a possible development
> of (nonsuper) bosonic string theory ???
I don't think so. The bosonic string is generally regarded as unphysical. On
the other hand, there are very interesting speculations that it may be just
another corner of the full theory and hence ultimately related to the
superstring:
http://golem.ph.utexas.edu/string/archives/000265.html#c000489
http://golem.ph.utexas.edu/string/archives/000265.html#c000490
Maybe others can say more about this.
P.S.
By the way, have you ever succeeded in showing that your hyperdiamond
checkerboard in 3+1 dimensions really reproduces the Dirac propagator?
Well show it. Put it down here for us to see. I personally don't believe
it, and want to see for myself.
drl
Thanks very much for an excellent reply, including references to two
string related visualizations of the photon.
Are similar visualizations of the electron possible?
Also, I reword another one of my earlier questions:
If U(1) contains only photons and not electrons, what is the similar
short name for the group which contains photons and electrons, but not
much else?
I am tempted to say, "the QED group" but I am not sure that is right
and I don't even know the proper name of the QED group. I presume it
has to be some subgroup of SU(2)xU(1), the GlashowWeinbergSalam
group, but that also includes W and Z, which I would like to exclude.
Thanks again for a very illuminating and very understandable post.
Jim Graber
> > LM ... string theory always contains gravity ...
Please don't ignore this key fact  the reason why we say (for example,
Witten says) that string theory *predicts* gravity. The nongravitational
theories are always just decoupling limits  i.e. limits where you turn
off gravity. If you only plan to believe me if I give you some references
or Polchinski's quotes, please feel free to ask. Gravity is always
contained as a vibration of a closed string, and closed strings can always
be created from open strings.
> When no Dbranes coincide there is just one massless vector on each,
> giving the gauge group U(1)^n in all.
This sentence means that "there are no other massless vectors", but it
certainly does not say that there are no other fields at all. A Dbrane
contains other massless states, e.g. the transverse scalars (and their
fermionic superpartners). It also contains an infinite tower of excited
massive states. Finally, a Dbrane in the full string theory is coupled to
the bulk which inevitably contains gravity as well as other fields and
particles.
> would 2 intersecting/coinciding D3 branes give U(2) gauge theory
> and 3 intersecting/coinciding D3 branes give U(3) gauge theory
> and 4 intersecting/coinciding D3 branes give U(4) gauge theory
Yes, but only if you talk about the coincident Dbranes. N coincident
Dbranes carry a U(N) gauge symmetry (and contain the appropriate gauge
N^2 bosons, as you explained). Moreover, if this stack of N Dbranes
approaches an orientifold, they meet their mirror images and U(N) is
extended to O(2N) or USp(2N).
The brane intersections also carry new types of matter  made of the open
strings stretched from one type of brane to the other  but these new
fields are *not* gauge fields, and they don't lead to new gauge
symmetries. For example, there are scalars whose condensation is able to
join two intersecting D2branes into a smooth, connected, hyperbolically
shaped objects (D2branes).
> Could you construct the Standard Model from D3 branes in
> bosonic string theory, letting up to 3 branes intersect:
> U(1) for photons
> U(2) for weak bosons
> U(3) for gluons
There are indeed very modern versions of the stringy Standard Models,
obtained from intersecting D6branes. There are many papers about it, let
me randomly choose a recent short one
http://arxiv.org/abs/hepth/0402087
The details are a bit more complicated than the simple description of
yours.
> Could the U(4) be a compact version of the U(2,2) Conformal Group
> that can give gravity by the MacDowellMansouri mechanism,
> as described by Mohapatra in section 14.6 of his book
> Unification and Supersymmetry, 2nd edition ???
I don't think so, but feel free to try.
> Could the U(5) be related to GUT physics ???
An SU(5) or U(5) can almost always be related to GUT physics, but you must
also get the right matter spectrum.
> Is there a physical reason to cut off the number of intersecting
> D3 branes at 3 or 4 or 5 ????
In general, there is no such reason. In more specific contexts, the number
of Dbranes can be determined or bounded by anomaly cancellation
and similar requirements. For example, the spacetime filling D9branes in
type I theory must generate the SO(32) gauge group, otherwise the theory
is anomalous. (There are other arguments for this choice of 16+16 branes,
too.)
> If you stop at the level of no more than 3 of the D3 branes
> intersecting, then would you get a unification of the standard model
> from the U(1), U(2), and U(3) with gravity, because, as Lubos Motl
> said, "... string theory always contains gravity ..." ???
The branes are not the whole picture. There are also closed strings whose
existence is independent of the Dbranes. The closed strings always exist
in any theory of open strings. Two open strings can join into one open
string (merging their endpoints), and the same local interaction can turn
an open string into a closed string. There is no way to avoid it, and
closed strings always contain a vibrational state that has all the
properties of a graviton.
There are also other ways how string theory generates gravity. For
example, a ddimensional conformal SU(N) gauge theory with a large value
of "N" is indistinguishable from the full string theory, dominated by
(super)gravity, in the antideSitter background in d+1 dimensions. This
is the content of "holography".
> Are there any papers that discuss such a possible development
> of (nonsuper) bosonic string theory ???
Yes, there are many papers of this sort, but the details what happen are
little bit different from what you wrote.
> Are similar visualizations of the electron possible?
Depending on how much you can stretch your imagination, yes.
States of the string which look like spin1/2 particles (in general) are in
their bosonic oscillator ground state but have 'spin field excitations'
turned on.
This first of all means that in terms of its spatial extension the string in
a spin1/2 particle state is in its gound state and hence oscillates as
little as allowed by quantum mechanics. Imagine a Gaussianshaped blob of
string.
But there are also the fermionic degrees of freedom on the superstring,
which I had mentioned before. For spin1/2 particle states of string these
are in what I propose here to call for pedagogical reasons a 'rotor
configuration'.
Ever heard of Hestenes' school of thought called 'Geometric Algebra'
(http://www.mrao.cam.ac.uk/~clifford/) where people are all excited about
how intuitively accessible spinors become when you make proper use of
Clifford algebraic notation?
The key idea of is that it is fun to think of Clifford algebra elements y^m
('gamma matrices') as vectors, think of products y^m y^n of them as little
planes ('bivectors') and realize that then
the object
exp(alpha y^m y^n /2 )
which is in the GA context sometimes called a 'rotor' is nothing but a
prescription to rotate things by an angle alpha in the plane spanned by y^m
and y^n  and is at the same time essentially a spinor!
To understand how this works see this message:
http://groups.google.de/groups?selm=a1euhh%24js0%241%40rs04.hrz.uniessen.de
.
Dont' proceed reading this post here until you have read the above one!
(and maybe related messages all summarized at
http://wwwstud.uniessen.de/~sb0264/spinorsDiraccheckerboard.html )


If what I describe in the posts at the links given above works for you and
gives you a way to visualize spinors then I can provide you with a
visualization of the spin1/2 particle state of an open superstring! In that
case, continue reading... :)


Now that you have a basic understanding of Clifford algebra and spinors
first note that the superstring is distinguished from the bosonic string by
the fact that at every point of the superstring there sits a little Clifford
generator ('gammamatrix'), which, as proposed in
http://groups.google.de/groups?selm=3E973BB4.273CFACD%40uniessen.de ,
can maybe roughly (very roughly, actually) be visualized by thinking of
little arrows at each point of the string:


\ < a generic piece of open bosonic string
\
\ _
 / \___
/ _/ \
\__/
<
<
v < a generic piece of open superstring
>
^ ^
^ < >>^<
> ^< <
v<<^
So in contrast to the spinning particle there is not just a single copy y^m
of the Clifford algebra (which contains in it all the information about
rotations and spinors) but a continuum of such representations y^m(s) at
every s, where s is a parameter running along the string. Which one of these
copies should we insert into the formula for a rotor given above in order to
get spinors?
The true answer involves concepts from superconformal field theory which are
not terribly easy to visualize. But what essentially happens in the
construction of 'worldsheet spin fields' is that you construct something
like
" H1(s) = int^s y^0(s') y^1(s') ds' "
" H2(s) = int^s y^2(s') y^3(s') ds' "
" H3(s) = int^s y^4(s') y^5(s') ds' "
" H4(s) = int^s y^6(s') y^7(s') ds' "
" H5(s) = int^s y^8(s') y^9(s') ds' " .
This is supposed to indicate that you take bispinors as before, at seperate
points on the worldsheet, and then integrate them from some reference point
to the point s on the string. The resulting 'integrated bispinor' is
conventionally called Hi, with i in {1,2,3,4,5. (This procedure of
integrating pairs of fermions is known as 'bosonization', essentially
because the result is an even graded object. I have omitted a conventional
factor of the imaginary unit from the definition of Hi as well as lots of
mathematical fine print).
My point here is that the Hi are in a way 'averaged' bivectors (in the
Clifford algebra sense) over the worldsheet. Please note very well the
quotation marks around the above five formulas are supposed to indicate that
they only transport (hopefully) the general idea, while the true definition
of these objects involves some technical subtleties which are however not
important at all for our current goal of trying to get a heuristic picture
of the spin1/2 particle state of the string.
So my point is that if you understand intuitively why for the ordinary
spin1/2 particle the rotor
exp( alpha1/2 y^0 y^1 + alpha2/2 y^2 y^3 + alpha3/2 y^3 y^4 + ....)
describes the spin degree of freedom of the particle (and the above links
should enable you to do just that) then you can now understand how the
'worldsheet spin field'
exp( sum_i alpha_i Hi(0) )
describes the analogous rotor for the superstring.
More precisely, if p,0> is the state of the superstring in which it has
centerofmass momentum p and all its oscillations are in its ground state
0>, then the state of the string which describes a spin1/2 particle looks
like
exp( sum_i alpha_i Hi(0) ) p,0> .
Very roughly and on a very heuristic level, what I am trying to say here is
that you can think of the superstring as a continuous chain of spin1/2
points whose 'averaged spin degrees of freedom produce the spin degree of
freedom of the string as a whole which makes it look like a spin1/2
particle'.
Finally note that all this is true for the open superstring. On the closed
superstring there is yet another copy of the Clifford algebra at every point
of the string and hence two different copies of the rotors/spin fields
above.
As soon as you understand how _two_ rotors define a differential form (see
http://wwwstud.uniessen.de/~sb0264/SpinorLie.html
for a simple introduction to this idea) you understand how acting with two
copies of such spin fields on p,0> you create a state of the _closed_
superstring which is the quantum of a pform field (a socalled RamonRamond
pform field).
These pform fields are essentially nothing but higherp generalizations of
ordinary electromagnetism. More on the latter can be found here:
http://wwwstud.uniessen.de/~sb0264/generalizedElectromagnetism.html .
On the closed superstring you can also apply one rotor/spin field and
instead of another such rotor turn on some of the oscillations of the
string. The result is partly a spinor (due to the rotor) and partly a vector
particle (due to the oscillations). This gives the gravitiono and dilatino
states of the string!
Finally, if anyone reading this is feeling the desire to understand the
subtleties and technical fine print which I have swept under the carpet, let
me point out the references:
The canonical textbook reference is section 10.3 of Polchinski's book. In
equation (10.3.13) the true definition of the 'string averaged bivectors' H
is given, while equation (10.3.29) gives the true definition of the 'string
rotor' which is usually called a 'spin field'.
Unfortunately crucial information about these spin fields is scattered all
over the second volume of Polchinski's book. For instance the crucial
formula which shows that the spin fields actually do behave as spinors under
multiplication with the Clifford elements y^m(s) is found in chapter 12,
equation (12.4.7).
The fact that a spinor is 'half a vector' is nicely expressed in the
absolutely crucial equation (12.4.18) of Polchinski's book. This formula
also describes the spacetime supersymmetry of the superstring, but in order
to understand that one must know about the meaning of 'superconformal ghost
picture changing'. In my humble opinion all this is best learned not from
Polchinski (where it is section 10.4 and the beginning of section 12.5) but
from the textbooklike seminal paper
D. Friedan & E. Martinec & S. Shenker,
Conformal invariance, Supersymmetry and String Theory,
Nucl. Phys. B271 (1986), 93165 .
But there was also another question that you asked:
> Also, I reword another one of my earlier questions:
>
> If U(1) contains only photons and not electrons, what is the similar
> short name for the group which contains photons and electrons, but not
> much else?
This is not the right question to ask. The electron couples to the gauge
bosons of the U(1) group. If you change that group, you change the number
and nature of species of gauge bosons, but not the number of species of
fermions.
But there is a short name for a theory of U(1) gauge bosons and electrons
'minimally coupled'. It's 'quantum electrodynamics' or QED for short!
> I am tempted to say, "the QED group"
If anything, the 'QED group' is U(1). The fact that there are electrons in
this theory is not captured by the nature of the group U(1) itself, however.
It is additional information.
> But actually, I am not sure that I understand the significance of this
> cancellation. On p. 229 of Polchinski it says
>
> "the tadpole is proportional to 2^13 \mp N. For the gauge group SO(2^13) =
> SO(8192) this vanishes, the tadpoles from the disk and the projective plane
> cancelling. For the bosonic string this probably has no special significance
> [...]".
>
> Maybe it depends on what John Baez wants to know from the D25 brane system
> whether this is a problem or not?
I think the point is that the bosonic string is so badly behaved
anyways, that a tadpole isn't a huge deal. The same cancellation in the
type one string forcest he gauge group to be SO(32) (as you probably
already know).
>
> Anyway, what about the D3 brane on an orbifold singularity? At least for the
> superstring I learn from hepth/0402160 that N D3 branes on the singularity
> of R^6(Z_2 x Z_2) give U(N) SYM with one supersymmetry on the 4d
> worldvolume. I'd guess that by exchanging the superstring for the bosonic
> string here we'd get U(N) YM without the superpartners. But I don't claim
> that I really understand this sufficiently.
Usually orbifold singularities give multiple copies of the gauge group
and matter in bifundamentals. I don't know that specific orbifold.
Aaron
On 20040308, John Baez <ba...@galaxy.ucr.edu> wrote:
> Here's a rather perversesounding question: has anyone figured
> out a way to give a stringy description of the usual quantized
> vacuum Maxwell equations on flat spacetime? No matter, no
> supersymmetry, no gravity... just photons? I know it sounds like
> using a sledgehammer to crush a fly, but I have reasons for being
> interested.
>
> I know people have tried to give a stringy description of pure
> YangMills theory, and this has been worked out in great detail
> for 2d YM theory, but remains mysterious in higher dimensions.
> To the extent that it works at all, it requires a different action
> than the usual Polyakov action.
>
> But, most of this work is on nonabelian YangMills theory!
> You'd think the comparatively trivial abelian case would be a
> lot easier: either it should definitely work, or definitely not work.
As I'm sure you know, breaking supersymmetry in string theory and
still having analytic control over lowenergy physics has been a
difficult problem. However, there are definite results.
If you don't mind about supersymmetry, there has been a huge amount of
research on how N=1 YangMills theories (with and without matter) can
be obtained from string theory. Most papers only explicitly mention
nonAbelian gauge groups, but the constructions usually extend to the
U(1) case upon setting N=1, which is mostly just considered too
trivial and uninteresting to mention.
As is now usual in string theory, there are a lot of dual descriptions
of the same physics. One of the first I'm aware of is hepth/9611090.
These constructions often go under the name of "Geometric engineering"
since they involve deriving properties of the low energy field theory
from the geometry of a curved space.
As others have pointed out, you can take string theory with a single
D3 brane, and the 4D field theory has N=1 supersymmetry with U(1)
gauge group, but 6 adjoint chiral superfields coming from the
transverse directions to the brane. You can give mass to these
scalars by compactifying the transverse dimensions on a suitable
curved space (see references below for precise details); if the
transverse directions are not flat then the brane cannot move freely
in these directions and the scalar fields obtain a mass. At energies
below this mass scale they'll decouple and you're left with U(1)
superMaxwell theory coupled to gravity. Gravity can also be
decoupled by taking a suitable scaling limit of the geometry.
See hepth/0103067 for a variation of this (again, they're mostly
concerned about U(N) because they can show how confinement emerges at
low energies from properties of the geometry; U(1) of course does not
confine). There they take D5 branes with 2 dimensions wrapped on a
compact cycle, leaving 3+1 large dimensions for the field theory to
live in.
Then there are the Tdual versions of this picture in terms of webs of
intersecting Dbranes; see some of the followups to hepth/9611230.
If you want to break supersymmetry, you can use Type 0 string theory
(an orientifold of type II that breaks supersymmetry; this introduces
a closed string tachyon, but it is possible to take a decoupling limit
that removes it from the gauge theory). See e.g. the recent review
0403071; the authors discuss a brane construction that gives rise to
nonsupersymmetric U(N) YangMills with a Dirac fermion in the 2index
(symmetric or antisymmetric) representation.
They are mostly concerned with obtaining results about QCD from
supersymmetric YangMills and string theory, but again, if you're
interested in more trivial questions then the triviality of the
2index representations of U(1) come to the rescue again.
Kris
> As I'm sure you know, breaking supersymmetry in string theory and
> still having analytic control over lowenergy physics has been a
> difficult problem. However, there are definite results.
As you all have probably seen, today a paper appeared which looks quite
relevant:
hepth/0403247:
Title: QED and String Theory
Authors: Shigeki Sugimoto, Kazuyoshi Takahashi
Abstract:
We analyze the D9D9bar system in type IIB string theory using Dpbrane
probes. It is shown that the worldvolume theory of the probe Dpbrane
contains twodimensional and fourdimensional QED in the cases with p=1 and
p=3, respectively, and some applications of the realization of these
wellstudied quantum field theories are discussed. In particular, the
twodimensional QED (the Schwinger model) is known to be a solvable theory
and we can apply the powerful field theoretical techniques, such as
bosonization, to study the Dbrane dynamics. The tachyon field created by
the D9D9bar strings appears as the fermion mass term in the Schwinger model
and the tachyon condensation is analyzed by using the bosonized description.
In the Tdualized picture, we obtain the potential between a D0brane and a
D8D8bar pair using the Schwinger model and we observe that it consists of
the energy carried by fundamental strings created by the HananyWitten
effect and the vacuum energy due to a cylinder diagram. The D0brane is
treated quantum mechanically as a particle trapped in the potential, which
turns out to be a system of a harmonic oscillator.
As another application, we obtain a matrix theory description of QED using
Taylor's Tduality prescription, which is actually applicable to a wide
variety of field theories including the realistic QCD. We show that the
lattice gauge theory is naturally obtained by regularizing the matrix size
to be finite.
The introduction begins as follows:
The interplay between string theory and quantum field theory has been one of
the most successful subject during the second revolution of the string theory.
There are many things that we can learn from it. For example, quantum field
theory often provides useful tools to study nonperturbative aspects of
string theory. Even though the nonperturbative formulation of string theory
is not available yet, we can analyze nonperturbative effects using the
techniques developed in the quantum field theory once we know the realization
of the quantum field theory in string theory. On the other hand,
we can apply various string duality (such as Sduality, Tduality, Mtheory,
open/closed duality, etc.) to quantum field theory. If we are lucky enough,
we would be able to obtain a new description of the quantum field theory.
However, most of the works along this line is done in supersymmetric
situations. Since our goal is to understand the real world, it would be
quite important to investigate nonsupersymmetric models.
One of the purpose of this paper is to analyze unstable Dbrane systems. by
using probe Dbranes. As a typical example, we consider the D9D9 system in
type IIB string theory and take a Dpbrane (p = 1, 3) as a probe.[2] As we will
explain in section 2, the worldvolume theory on the Dpbrane contains (p+1)
dimensional QED.
The realization of the four dimensional QED in string theory could be
interesting since it is a realistic system. It would be interesting if we could
say something realistic using string theory, though we will not consider
much about it in this paper.
> As you all have probably seen, today a paper appeared which looks quite
> relevant:
>
> hepth/0403247:
> Title: QED and String Theory
The mind reels at the hubris and lack of shame.
I'm sorry, this is not QED. And if the proposed work is what we can
expect from the "real" TOE  well, no comment.
drl
In article <N2K8c.10941$WH5....@newssvr22.news.prodigy.com>,
Danny Ross Lunsford <antima...@yahoo.NOSEPAM.com> wrote:
> Urs Schreiber wrote:
>
> > As you all have probably seen, today a paper appeared which looks quite
> > relevant:
> >
> > hepth/0403247:
> > Title: QED and String Theory
>
> The mind reels at the hubris and lack of shame.
Hubris? Lack of shame? What on earth are you referring to?
>
> I'm sorry, this is not QED. And if the proposed work is what we can
> expect from the "real" TOE  well, no comment.
Quoting from the abstract:

It is shown that the worldvolume theory of the probe Dpbrane contains
twodimensional and fourdimensional QED in the cases with p=1 and p=3,
respectively, and some applications of therealization of these
wellstudied quantum field theories are discussed.

They claim to exhibit a string theoretical system which contains QED. Do
you have a problem with that?
Aaron
Part of it is. The rest decouples.
> And if the proposed work is what we can
> expect from the "real" TOE  well, no comment.
It should maybe be emphasized that what is presented in that paper is not
supposed to be a TOE solution of string theory, i.e. not a solution of
string theory which is supposed to describe all aspects of nature that we
observe.
Rather, as is discussed in the introduction, the authors investigate aspects
of the fascinating fact that many field theories can be regarded as certain
limits of certain configurations in string theory. They set out to find a
particular such configuration which in the appropriate limit contains QED
plus other, decoupled, sectors.
The point is that having the stringy description of a field theory, thus
embedding the field theory into a larger context, allows to use knowledge of
string theory to gain understanding of field theory. In particular, the
authors of the above paper discuss how Tduality in the stringy description
leads to matrix descriptions and lattice regularizations on the field theory
side.
That's comparable to how embedding the reals into the complex numbers allows
insights into real analysis. You don't have to believe that complex numbers
are real ;) for this to be useful. Similarly you don't have to believe that
strings are real for stringy descriptions of field theory to be useful.
I'd like to come back to John Baez' original question.
Equation (2.3) of the above paper tells us that the lowenergy effective
worldvolume theory of a Dp brane which propgates in a 10d Minkowski
background which is completely filled with N spacefilling D9 branes and
their antibranes is QED with several 'flavors' plus a decoupled sector of
free scalars and spinors, all on the flat and (in this limit) undynamical
background of the Dp brane.
Since the extra scalars (and spinors, since this comes from superstring
configurations) are decoupled, we can just as well ignore them if we are
only interested in the QED part. And by sending the gauge coupling to 0
(proportional to the string coupling for p=3) I assume one can also ignore
the QED fermions. Restricting to a single Dp brane then should indeed give
the answer that John Baez was looking for. (The tadpole anomalies are dealt
with in this framework, the scalars and extra spinors are decoupled.)
But I am prepared to be made aware of further subtleties... :)
Urs Schreiber wrote:
> Part of it is. The rest decouples.
And this means?
> Rather, as is discussed in the introduction, the authors investigate aspects
> of the fascinating fact that many field theories can be regarded as certain
> limits of certain configurations in string theory. They set out to find a
> particular such configuration which in the appropriate limit contains QED
> plus other, decoupled, sectors.
There is *nothing* in this paper that even *resembles* QED in any
representation that I know of. Whatever it is, it is *not* QED.
> The point is that having the stringy description of a field theory, thus
> embedding the field theory into a larger context, allows to use knowledge of
> string theory to gain understanding of field theory. In particular, the
> authors of the above paper discuss how Tduality in the stringy description
> leads to matrix descriptions and lattice regularizations on the field theory
> side.
>
> That's comparable to how embedding the reals into the complex numbers allows
> insights into real analysis. You don't have to believe that complex numbers
> are real ;) for this to be useful. Similarly you don't have to believe that
> strings are real for stringy descriptions of field theory to be useful.
I'm sorry as a physicist I cannot accept any of this, any more than I
can return to belief in epicycles. It is physically painful to see such
claims as are made here.
> I'd like to come back to John Baez' original question.
>
> Equation (2.3) of the above paper tells us that the lowenergy effective
> worldvolume theory of a Dp brane which propgates in a 10d Minkowski
> background which is completely filled with N spacefilling D9 branes and
> their antibranes is QED with several 'flavors' plus a decoupled sector of
> free scalars and spinors, all on the flat and (in this limit) undynamical
> background of the Dp brane.
First of all, there is nothing in this paper that can properly be called
a calculation. It is symbol salad sprinkled with buzzwords bits.
In the course of this exercise in evanescence, an action is posited with
suspiciously indexed objects formed from mystery spinors and a gauge
field willynilly cast into a somewhat suggestive form. THIS IS NOT QED.
> Since the extra scalars (and spinors, since this comes from superstring
> configurations) are decoupled, we can just as well ignore them if we are
> only interested in the QED part. And by sending the gauge coupling to 0
> (proportional to the string coupling for p=3) I assume one can also ignore
> the QED fermions. Restricting to a single Dp brane then should indeed give
> the answer that John Baez was looking for. (The tadpole anomalies are dealt
> with in this framework, the scalars and extra spinors are decoupled.)
>
> But I am prepared to be made aware of further subtleties... :)
Here are some words: vacuum, antiparticle, magnetic moment,
polarization, effective mass, fine structure constant. They are words
from physics. All are very definite things. None of them shows up
anywhere in this paper. Now, these two are making a rather bold claim 
that a theory with 20 years of utter failure and still without a defined
vacuum, contains the most successful phenomenological theory ever. You
might think that such a bold claim might at least induce one of them to
calculate the Lamb shift. But this is too much to expect I suppose.
I am sorry, I can no more accept this kind of "physics" any more than I
could endorse a return to heavenly epicycles, orbs, and ethers sponsored
by the Young Geocentric Republicans.
drl
If you really didn't want to comment, you wouldn't have.
Critics of string theory often complain that it has demonstrated no
relevance for real physics. Now you're complaining that a paper
explaining how aspects of QED might be understood from string theory
is "hubris" and "shameless".
There's really just no pleasing some people.
Kris
Danny Ross Lunsford <antima...@yahoo.NOSEPAM.com> wrote in message news:<N2K8c.10941$WH5....@newssvr22.news.prodigy.com>...
The key statement is at the end of Urs Schreiber's post:
> There is *nothing* in this paper that even *resembles* QED in any
> representation that I know of. Whatever it is, it is *not* QED.
I am not sure which representations you are referring to. Usually field
theories are defined by writing down their action functionals. As you know,
the action of QED looks schematically like
S_QED = int ( F^2 + i psibar D psi  m psibar psi ) d^4 x,
where F is the electromagnetic field strength, psi is the fermion and D the
gauge covariant Dirac operator.
(For those reading this who do not know this action, this can for instance
be found discussed in the context of equation (4.4) of the book
M Peskin, D. Schroeder, An Introduction to Quantum Field Theory (Perseus) )
If you compare this with equation (2.3) of the paper that we are discussing
then you see that the action given there is just the above action of QED
(the first two terms) plus the action of free scalars and spinors (the last
two terms).
Note that in equation (2.3) the spinors are massless, but that they acquire
a mass when the coupling to the condensing tachyon is taken into account in
equation (2.7).
(There is a tachyon in this stringy setup because the configuration
consisting of branes and antibranes is unstable and wants to decay. As this
decay process takes place the vev of the tachyon field increases  the
tachyon 'condenses' until the stable vacuum is reached.)
> "Danny Ross Lunsford" <antima...@yahoo.NOSEPAM.com> schrieb im
> Newsbeitrag news:RwU8c.11016$qH1....@newssvr22.news.prodigy.com...
>
>
>>There is *nothing* in this paper that even *resembles* QED in any
>>representation that I know of. Whatever it is, it is *not* QED.
>
>
> I am not sure which representations you are referring to. Usually field
> theories are defined by writing down their action functionals. As you know,
> the action of QED looks schematically like
>
> S_QED = int ( F^2 + i psibar D psi  m psibar psi ) d^4 x,
mm yes Urs, I know the canonical Lagrangians for lots of theories..
> where F is the electromagnetic field strength, psi is the fermion and D the
> gauge covariant Dirac operator.
>
> (For those reading this who do not know this action, this can for instance
> be found discussed in the context of equation (4.4) of the book
> M Peskin, D. Schroeder, An Introduction to Quantum Field Theory (Perseus) )
>
> If you compare this with equation (2.3) of the paper that we are discussing
> then you see that the action given there is just the above action of QED
> (the first two terms) plus the action of free scalars and spinors (the last
> two terms).
2.3 is not an "equation"  it is simply written down without motivation,
or with cabalistic motivation known only to stringers, and moreover the
resemblance to QED is completely superficial  after all, what else can
you *do* with a spinor field and a vector field and a Clifford algebra?
The Lagrangians of *all* traditional quantum field theories look like
this. It would be far better if your action looked *completely
different* but, after a *physical limiting argument*, was shown to take
the form of the QED Lagrangian *in detail*, not "sort of". This is how
real physics works.
> Note that in equation (2.3) the spinors are massless, but that they acquire
> a mass when the coupling to the condensing tachyon is taken into account in
> equation (2.7).
TACHYONS???
> (There is a tachyon in this stringy setup because the configuration
> consisting of branes and antibranes is unstable and wants to decay. As this
> decay process takes place the vev of the tachyon field increases  the
> tachyon 'condenses' until the stable vacuum is reached.)
I have nothing more to say about this paper.
drl
> mm yes Urs, I know the canonical Lagrangians for lots of theories..
Well, sorry, I just didn't know how to interpret your statement that you
couldn't see anything that resembles QED in this paper.
> 2.3 is not an "equation"  it is simply written down without motivation,
I realize that you have strong feelings concerning this paper. But it also
seems to me that your criticism is essentially that you do not see how the
formulas in that paper are derived.
Of course the authors do not reiterate all the standard steps of the theory.
For instance in order to understand how equation 2.3 follows from the
assumptions at the beginning of the paper one uses the general results about
low energy effective field theories of branes. The most important
ingredients that one needs can be found in section 8.7 of Polchinski's book.
In particular see equations (8.7.2) and (13.3.34). More pedagogic
derivations of these steps are given in many lecture notes, for instance
those by Szabo. For a link list of these lecture notes see
http://golem.ph.utexas.edu/string/archives/000327.html .
Also, over at sci.physics.strings, which has been created today, there is a
new thread where people try to get a better understanding of the paper that
we are talking about here. I invite everybody interested to have a look.
> Hubris? Lack of shame? What on earth are you referring to?
If it is not selfevident there is no point in explaining it.
>>I'm sorry, this is not QED. And if the proposed work is what we can
>>expect from the "real" TOE  well, no comment.
>
>
> Quoting from the abstract:
> 
> It is shown that the worldvolume theory of the probe Dpbrane contains
> twodimensional and fourdimensional QED in the cases with p=1 and p=3,
> respectively, and some applications of therealization of these
> wellstudied quantum field theories are discussed.
> 
>
> They claim to exhibit a string theoretical system which contains QED. Do
> you have a problem with that?
Yes. I scanned the paper. It is QED, minus E and D. That is, only
technical details are missing.
It utterly astonishes me that anyone takes this seriously.
drl
Well nowadays amidst all Dbrane constructions of gauge theories,
somehow people seem to believe that Dbranes are essential for gauge
symmetry, whereas gauge symmetries are known to arise also from
closed strings since almost 20 years.
Of course, the most basic field theories can also be realized by
the most basic string backgrounds  as Lubos pointed out in his
first post, just a simple toriodal compactification produces an
abelian gauge theory, and the stringy stuff can be decoupled by
sending alpha' away; no Dbranes are necessary. The effective action
is easy to compute and leads to pure U(1) gauge theory, in the
appropriate limits.
String theorists were eager to challenge the LQG people to
quantize the string. A similar challenge would be to compute real
QED results, like the Lamb shift or the electron's anomalous
magnetic moment, from string theory.
Seriously, I think this would be a nice thing to do, and if you
succeed it would be a major breakthrough for string theory. I
don't really see why it should be so hard. After all, you can
compute graviton scattering amplitudes in string theory, at least
to second order, and here we talk about electronphoton
amplitudes, which if anything should be easier to calculate.
I would expect the string result to be close to the QED result
but not exactly equal to it, since string theory should
automatically include contributions from gravitons and other
particles. So the real challenge would be to calculate the
difference between QED and string estimates for the Lamb shift
and mu_e.
If you can't do that, you should at least tell Ed Witten to stop
claiming that string theory is more predictive than field theory.
This sounds as if string theory should predict the mass of the electron.
This would be a very interesting test of string theory. Would it also
predict the fine structure constant?
I am looking forward to seeing more detailed calculations with
predictive value.
Arnold Neumaier
> String theorists were eager to challenge the LQG people to
> quantize the string. A similar challenge would be to compute real
> QED results, like the Lamb shift or the electron's anomalous
> magnetic moment, from string theory.
>
> Seriously, I think this would be a nice thing to do, and if you
> succeed it would be a major breakthrough for string theory.
Hardly. All the above are essentially trivial. The problem, as usual, is
that string theory does not predict the value of various fundamental
constants. The functional forms, however, are straightforward.
[...]
> I would expect the string result to be close to the QED result
> but not exactly equal to it, since string theory should
> automatically include contributions from gravitons and other
> particles. So the real challenge would be to calculate the
> difference between QED and string estimates for the Lamb shift
> and mu_e.
There are corrections. They are also well understood. They're controlled
by a parameter so as to be undetectably small (obviously) in any
realistic model.
> If you can't do that, you should at least tell Ed Witten to stop
> claiming that string theory is more predictive than field theory.
In fact, string theory amplitudes existed even before string theory did.
Aaron