Super-Strings
Adam Walsh
ciao!
-:: Walsh ::-
SCOTT I CHASE
>Pardon My ignorance but what is a Super String?
Strings are supposed to be the fundamental objects in the
Universe, microscopic 1-dimensional loops of stuff which look like
zero-dimensional point objects at suffiently poor resolution.
Superstrings are strings with a Supersymmetric Lagrangian. I hope
that this helps. :-)
-Scott
--------------------
Scott I. Chase "It is not a simple life to be a single cell,
SIC...@CSA2.LBL.GOV although I have no right to say so, having
been a single cell so long ago myself that I
have no memory at all of that stage of my
life." - Lewis Thomas
Andrew - Palfreyman
Occam's Razor in action, or is it perhaps something at a deeper
level? I mean that one could just as easily have chosen a primitive
of higher dimensionality.
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| lord snooty @the giant | inceptus clamor frustratur hiantes |
| poisoned electric head | andrew_-_...@cup.portal.com |
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Benjamin Weiner
A SuperString is made out of the same material as a SuperBall, those
cute little bouncy things. Physics graduate students who know that
the first problem in the _Princeton Problems in Physics_ is about a
SuperBall will no doubt be happy to hear that the first problem in the
forthcoming second edition is about a superstring ...
OK, dumb jokes aside, superstrings are a candidate for a theory that
explains, more or less, all the fundamental interactions of physics;
a reference at a popular level is the book "Superstrings: A Theory of
Everything?" The "string" part is that these theories consider
fundamental particles to be strings rather than points, with the
dimension of the string being incredibly small; the theory is often
characterized as having a lot of dimensions with the extra dimensions
being "rolled up," leaving only the 3+1 of ordinary spacetime. It has
the attraction of maybe being the Big Mama of particle theory that
finally explains it all, but it is fiendishly complicated.
The "super" part is something called supersymmetry, which is popular
in "everyday" particle physics as well; in it, there is a symmetry
between fermionic (loosely, particles like quarks and electrons; the stuff
of ordinary matter) and bosonic particles (loosely, particles that
carry the interactions/forces, like the photon). So each fermion
has a boson partner, and vice versa. No such partner particles have yet
been discovered, though.
I hope this has been informative and not misleading, because
string theory is "not my department." (inside joke, sorry)
David E. Brahm
> I wonder if the fad with string theory and superstrings is simply
> Occam's Razor in action, or is it perhaps something at a deeper
> level? I mean that one could just as easily have chosen a primitive
> of higher dimensionality.
One could, and people do ("super-membrane theory"), but there is something
particularly nice about 1+1 dimensions (the world sheet of a string),
called (I believe) conformal invariance. Whenever you write an action in
curved spacetime, it looks like
S = \int d^D x \sqrt{g} g^{\mu \nu} ...stuff...
where "g" is the determinant of g_{\mu \nu}, the inverse of the metric. In
2D, the metric has 3 degrees of freedom, but 2 can be eliminated by
coordinate transformations; what remains can be written
g^{\mu \nu} = \eta^{\mu \nu} e^\phi
where "\eta" is the Minkowski (flat) metric. Then "g" is proportional to
e^{-\phi}, and "\phi" drops out of S! This only works in 2D, and is
important to the rest of the development of string theory. See Green,
Schwartz & Witten p.23 (that's about as far as I ever got in it! :-)
Furthermore, 2D is better than 1D (the world lines of point particles)
because 1D interactions (e.g. one particle splits into two) occur at a
single spacetime point, which can lead to singularities and infinities.
String interactions, on the other hand, are not localized to a point.
So conformal invariance and finiteness are the nice features of strings.
--
Staccato signals of constant information, | David Brahm, physicist
A loose affiliation of millionaires and | (br...@cco.caltech.edu)
billionaires and Baby ... |---- Carpe Post Meridiem! --
These are the days of miracle and wonder, | Disclaimer: Forgive me, Lord,
And don't cry, Baby, don't cry, don't cry. | I have defended String Theory.
Matthew P Wiener
>One could, and people do ("super-membrane theory"),
For some reason, the membrane is always a p-dimensional object. They
are called p-branes for short. This is not a joke.
--
-Matthew P Wiener (wee...@sagi.wistar.upenn.edu)
Allen Knutson
>Furthermore, 2D is better than 1D (the world lines of point particles)
>because 1D interactions (e.g. one particle splits into two) occur at a
>single spacetime point, which can lead to singularities and infinities.
>String interactions, on the other hand, are not localized to a point.
There's another, even more compelling, reason to like higher-dimensional
objects. In a Feynman diagram showing two particles merging (say, an
electron absorbing a photon), there's a great difference between the
parts of the diagram where the individual particles are propagating, and
the nasty Lorentz-invariant vertex where they meet. But if the objects
are strings, the interaction looks like a pair of pants, a nice smooth
2-manifold all over, no unpleasant separation into "propagation" and
"interaction".
(By the way, this "pair of pants" terminology is now very standard -
people speak of "pants decompositions" of higher-genus surfaces, and so on.)
Which makes me wonder, what could one accomplish with a theory whose
elementary constituents were inseparable _pairs_ of points? It keeps the
nice features described above, for starters - (a,a') interacts with (b,b')
to produce the new particle (a,b'). Allen K.
Matt McIrvin
>There's another, even more compelling, reason to like higher-dimensional
>objects. In a Feynman diagram showing two particles merging (say, an
>electron absorbing a photon), there's a great difference between the
>parts of the diagram where the individual particles are propagating, and
>the nasty Lorentz-invariant vertex where they meet. But if the objects
>are strings, the interaction looks like a pair of pants, a nice smooth
>2-manifold all over, no unpleasant separation into "propagation" and
>"interaction".
And now, another idiot question. When I talk to string theorists, they
keep talking about something called "the string coupling constant."
If interaction vertices have been banished and all we have are pairs
of pants, what is this? It seems to be different from the "string
tension," which is what I would imagine would be the relevant
quantity if these things are all propagator.
>Which makes me wonder, what could one accomplish with a theory whose
>elementary constituents were inseparable _pairs_ of points? It keeps the
>nice features described above, for starters - (a,a') interacts with (b,b')
>to produce the new particle (a,b'). Allen K.
This reminds me of strong meson interactions in the large-N (large gauge
group) limit. The mesons are quark-antiquark pairs that are bound by very
stringlike fields. The leading diagrams are flat sheets with quarks going
around the edges and planar networks of gluon lines in the interior.
It starts to become apparent why open string theory gave a good
early description of hadrons. Apparently, according to Gross
(he gave a talk here last week), in two dimensions QCD is quite literally
a string theory.
--
Matt McIrvin
john baez
>lordS...@cup.portal.com (Andrew - Palfreyman) writes:
>> I wonder if the fad with string theory and superstrings is simply
>> Occam's Razor in action, or is it perhaps something at a deeper
>> level? I mean that one could just as easily have chosen a primitive
>> of higher dimensionality.
>
>One could, and people do ("super-membrane theory"), but there is something
>particularly nice about 1+1 dimensions (the world sheet of a string),
>called (I believe) conformal invariance.
Yes, people have studied "p-branes," but they are supposedly much less
well-behaved; when you quantize them they give infinities that people
apparently have not been able to renormalize away.
Also: the world sheet of a string is not just 2-dimensional, it's a
Riemann surface. This is where the conformal invariance comes in. Recall
how in E&M you used conformal invariance of 2d electrostatics to solve
the Laplace equation with weird boundary conditions? You were tapping
the power of the conformal group, which is infinite-dimensional in
the 2d case. There is so much powerful mathematics associated with
Riemann surfaces that it is natural to want to use it... and this is
what people have done (greatly pushing forward the subject in the
process). Of course, it's not clear whether Nature finds this mathematics
as tempting as we do.
Steve Carlip
>I wonder if the fad with string theory and superstrings is simply
>Occam's Razor in action, or is it perhaps something at a deeper
>level? I mean that one could just as easily have chosen a primitive
>of higher dimensionality.
There is, in fact, some work on "membrane theory," the higher dimensional
generalization of string theory. In general, membranes don't work very
well for particle physics purposes. For instance, strings have a
discrete energy spectrum, yielding particle-like excitations of
different masses; membranes typically have a continuous spectrum,
and would lead to a continuous range of particle masses.
There may now be ways of fixing this --- I'm not up on the most
recent literature.
Steve Carlip
car...@dirac.ucdavis.edu
brett mcinnes
:
: Yes, people have studied "p-branes," but they are supposedly much less
: well-behaved; when you quantize them they give infinities that people
: apparently have not been able to renormalize away.
One problem with 2-branes is that at some point you need to know whether
the Poincare conjecture is true. I recall reading the following amusing
exchange:
Q: How are you going to proceed without the Poincare conjecture?
A: Well, if I were Ed Witten I'd turn that around, and give you a
brane-theoretic proof of the Poincare conjecture..........[laughter].
Gordon C Joly
>[...]There is so much powerful mathematics associated with
>Riemann surfaces that it is natural to want to use it... and this is
>what people have done (greatly pushing forward the subject in the
>process). Of course, it's not clear whether Nature finds this mathematics
>as tempting as we do.
It is also not clear whether spacetime is "foam" or not (that is to
say has a Winding number of one).
There is an assumption that we live in a (continuously) differential
manifold, which may not be the case.
Gordon.
--
Gordon Joly Phone +44 71 387 7050 ext 3703 FAX +44 71 387 1397
Internet: G.J...@cs.ucl.ac.uk uca...@ulc.ac.uk
Computer Science, University College London, Gower Street, LONDON WC1E 6BT
Bryan Carpenter
>I wonder if the fad with string theory and superstrings is simply
>Occam's Razor in action, or is it perhaps something at a deeper
>level? I mean that one could just as easily have chosen a primitive
>of higher dimensionality.
There definitely is more to it than that. People naturally tried
playing around with higher dimensional membranes when string theory
became fashionable, but I don't think they worked particularly well.
Superstrings have nice mathematical properties, which are supposed
to be connected with the special structure of the conformal group
in 2 dimensions (1 space + 1 time). But, it's a long time since I learnt
anything about strings, so I'm not going to risk saying any more...
> --------------------------------------------------------------------------
>| lord snooty @the giant | inceptus clamor frustratur hiantes |
>| poisoned electric head | andrew_-_...@cup.portal.com |
> --------------------------------------------------------------------------
Bryan
Matthew P Wiener
>There definitely is more to it than that. People naturally tried
>playing around with higher dimensional membranes when string theory
>became fashionable, but I don't think they worked particularly well.
The only mathematical feature in p-brane theory that I could understand
(which isn't saying much) was that the acceptable theories corresponded
with R,C,Q,O. That was cool.
John C. Baez
>In article <25...@galaxy.ucr.edu> ba...@guitar.ucr.edu (john baez) writes:
>>[...]There is so much powerful mathematics associated with
>>Riemann surfaces that it is natural to want to use it... and this is
>>what people have done (greatly pushing forward the subject in the
>>process). Of course, it's not clear whether Nature finds this mathematics
>>as tempting as we do.
>
>It is also not clear whether spacetime is "foam" or not (that is to
>say has a Winding number of one).
"Winding number" is a number associated to a continous function from the
circle to itself, that counts how many times it wraps around (with
sign). It doesn't really make sense to say that spacetime has winding
number 1.
Your point about the implicit assumption in conventional string theory
that spacetime is a manifold is correct, though. If spacetime is not a
manifold (the idea of "spacetime foam"), we have rather little idea of
what it is. My hunch is the answer will be "yes and no". Sometime I
should go into this...