Conceptual question
Lubos Motl
news:Pine.LNX.4.31.040328...@feynman.harvard.edu...
> Since there are so many possible vacuum states in string theory, with many
> different possible compactifications and configurations of background
> D-branes, should (in your opinions) the "final" non-perturbative string
> theory/M-theory restrict it down to a few or even
> just one vacuum state or will there always be freedom in model building?
This is, of course, one of the most important questions of superstring
phenomenology nowadays. A well-known founder of string theory (L.S.) is now
writing a book about his recent "discovery" called the "stringy landscape".
There exists a growing evidence that the number of metastable vacua in
string theory is very large, and therefore one might be forced to adopt at
least some aspects of the anthropic thinking.
The most successful industry of propaganda, that tries to argue that we know
almost for sure that the number of vacua is huge, was started by KKLT
http://arxiv.org/abs/hep-th/0301240
Of course, many of us are highly irritated by the idea that we would have to
adopt the anthropic principle. Some people are approaching these questions
scientifically, some people approach them less scientifically. Even if the
number of vacua is large, as some people argue, it might be that the allowed
cosmologies are much more constrained. Even if the number of cosmologies is
large, the predictivity does not have to be lost. Two famous physicists
(N.A-H. and S.D.) are now working on their amazing predictions for the LHC
accelerator - if this prediction is confirmed, they say, you will have to
believe that the landscape is reality.
I hope that the start of the LHC will remove a lot of unconstructive ideas
at the end. It is just not certain which ideas are constructive and which
ideas are not.
Wolfgang Lerche
> This is, of course, one of the most important questions of superstring
> phenomenology nowadays. A well-known founder of string theory (L.S.) is now
> writing a book about his recent "discovery" called the "stringy landscape".
> There exists a growing evidence that the number of metastable vacua in
> string theory is very large, and therefore one might be forced to adopt at
> least some aspects of the anthropic thinking.
Well, what I find irritating is that these ideas are out since the
mid-80's; in one paper on 4d string constructions a crude estimate
of the minimal number of string vacua was made, to the order 10^1500;
this work had been ignored (because it didn't fit into the philosophy
at the time) by the same people who now re-"invent" the landscape,
appear in journals in this context and even seem to write books
about it. There had always been proponents of this idea, which is
not new by any means. Surely the number of 4d string constructions
has vastly increased since that time, and they have been become much
more sophisticated, but that's only a quantitative change; the whole
discussion could (and in fact should) have been taken place in
1986/87. The main thing what has changed since then is the mind
of certain people, and what you now see is the Stanford propaganda
machine working at its fullest.
> The most successful industry of propaganda, that tries to argue that we know
> almost for sure that the number of vacua is huge, was started by KKLT
>
> http://arxiv.org/abs/hep-th/0301240
Indeed...
Shamit Kachru
me to explain what I was interested in exploring, in that paper, in my
previous works on related subjects, and in my ongoing work on the subject.
It has been clear since the mid 1980s and even clearer since the mid 1990s
that string theory has many many exact vacuum states with extended
supersymmetry (continuous moduli spaces of them, in fact), and
calculations of their properties provide many of us with amusement.
However, the more interesting situation is that with little or no
supersymmetry.
In the case with say $N=1$ supersymmetry below the compactification
radius, a natural question is, how is the vacuum degeneracy lifted? And
if and when it is lifted, what are the properties of the resulting vacua?
For many years it was more or less assumed that the moduli in typical
constructions are only lifted by non-perturbative effects. More recently
it has become clear that "generic" constructions (in a technical sense I
will be happy to make precise) actually have computable potentials for
many of the moduli already at tree level, and it has been an interesting
exercise to compute these potentials and characterize the resulting vacua.
These potentials are generated by magnetic fluxes in the extra dimensions,
and as I said, they are generically present; the number of models
including such fluxes is much much larger than the number without, as far
as anyone can tell.
Following the work of Bousso and Polchinski and others, it became clear
that the NUMBER of flux models can be very large, and that furthermore
this can be a USEFUL thing. All of these models still have some moduli
fields left over; these are expected to generically receive potentials
from combinations of worldsheet and D-brane instantons, depending on the
specific class of constructions (by "generically," I mean that such
effects are known to exist, and no symmetry forbids them from appearing in
most models, so they should). However, in a SMALL fraction of the flux
models, it seems likely that small parameters resulting from the careful
choice of the background fluxes can be used to find vacua (after including
these further effects) that remain in a controllable regime of parameters,
i.e. at weak coupling and relatively large radius.
I think it is fair to say that these points involving control over moduli
potentials (and hence countings of models with no moduli, as opposed to
constructions based on worldsheet CFT which are parts of moduli spaces
that will be lifted) are things that make the discussion today more
sophisticated than the one that could have occurred in the mid 1980s.
The points of the KKLT paper as far as I know included that argument and a
few more:
-- that in "generic" flux models (where the genericity is being applied in
the ways mentioned above), one can expect to find AdS vacua with no
moduli; and in a fraction of these the compactification radius can be
large enough for control but << the AdS radius (so indeed there is a sense
in which the model is a 4d model, unlike the standard AdS/CFT
constructions where the size of the compactification is the same as the
AdS radius).
-- and that by including further plausible ingredients, roughly D-terms in
the 4d $N=1$ supersymmetric language, a small fraction of these vacua
should admit moderately controllable lifts to deSitter space. By
moderately controllable, I mean that couplings can be relatively weak, and
the barrier height for the dS decay can be high compared to expected
radiative corrections to the potential.
While I consider it completely obvious that string theory has many vacua
and that dS models should exist within string theory, the KKLT paper was
written in an environment (contrary to what Wolfgang seems to imply) where
some of these facts were (and are) under active debate. For instance very
famous figures in our field were saying quite publicly in the recent past
that string theory is incompatible with deSitter space; and various no-go
theorems were proved which show that unless one really uses many of the
ingredients of string theory (instead of just the simplest ingredients of
supergravity), one cannot find dS constructions. So indeed it was an open
challenge to refute this growing dogma at least as I perceived it, and the
KKLT paper was meant to show that simple genericity arguments together
with the ideas of Bousso and Polchinski allow one to argue strongly that
dS vacua should exist.
As far as the science goes, it seems to me the clearest directions for
work involve either finding examples where more pieces of the
superpotential are exactly calculable (about which I have some ideas which
I am pursuing with collaborators here, and which closely ties to a ton of
work that people who work on topological strings are doing), or finding
out whether there are simple characterizations of just the pieces we do
understand. For instance, we know by now that in the no-scale
approximation there are many flux vacua; far too many to study each
individually. But it may be that simple hypotheses (which are testable)
suffice to characterize the statistical properties of these vacua. As an
example: Douglas has conjectured a very specific distribution of vacua on
the Calabi-Yau moduli space (in this no-scale approximation in the IIB
theory); this conjecture is testable, and I am actually testing it now
with various collaborators by constructing an extremely large set of
models in a specific Calabi-Yau and comparing the distribution to the
prediction. Further work along these lines can test whether or not the
small parameters one needs for parametric control in a fraction of the
flux vacua do indeed arise with some frequency in the large set of flux
vacua; we have a prediction for the distribution of one of these control
parameters, the gravitino mass in the no-scale approximation, and we can
test this as well. As an illustration of how this kind of thing can be
useful, I can point to the work of Candelas in the distant past, where
some beautiful and timely plots of Calabi-Yau hodge numbers provided one
of the most suggestive pieces of early evidence for mirror symmetry.
So anyway my attitude is that genericity suggests this landscape is there,
we need to characterize its properties, and we have (right now) some
interesting things to do in this direction.
It seems true that this picture implies that there will be no beautiful
prediction for the cosmological constant (CC) and hence some people will
like to invoke the anthropic principle. I don't have much to say about
that, except that I see nothing wrong with their thinking; they may well
be right that there is no other explanation for the CC, just as there is
no other explanation for why we live on the earth instead of venus. But my
own interest would be in seeing what properties of the world string theory
allows us to make firm predictions about, so to me the thing to do is to
sort out which things are "accidental" and which aren't, and focus on the
latter.
I am not exactly sure where Wolfgang's "Stanford publicity machine" is
involved in this project, but I will be happy to hear about it from him.
As far as I know, my papers go to hep-th like everyone elses. :)
Lubos Motl
> Hmm. Well, as an author of the KKLT paper, I think it may be useful for
> me to explain what I was interested in exploring, in that paper, in ...
Dear Shamit, I liked your entertaining and insightful description and many
statements in your posting are hard to be questioned, but as you know, it
does not make me like the anthropic reasoning. (I don't use the word
"principle", because this thing is certainly not a principle: it is rather
an "anthropic lack of principles", as we started to call it.)
Imagine that you would be hired to use all of your intelligence - that you
displayed not only in KKLT or KKLMMT etc. :-) - to compose a group of
physicists, combine all arguments, branes, instantons, terms and other
weapons that you can imagine, convert some of them into equations, and
construct a paper that would lead to the opposite conclusion, namely that
based on the insights of the 1990s, the landscape is very small and one
should expect that the Universe without unbroken SUSY is essentially
guaranteed to collapse into one of a very small number of dS-like vacua.
Your strategy will be, of course, to use as many conceivable (and new)
anomalies and decay channels of the backgrounds to eliminate them; using
all conceivable dualities to relate them to one another; arguing that the
stable vacua tend to be on the very special and rare symmetry points; that
the large fluxes always create too much energy density or destroy the
manifold; you will be inspired by Tom Banks's et al. papers suggesting
that various the generic backgrounds are inconsistent with many things we
know so that the semi-realistic vacua are already hugely limited; you will
create a picture in which the "canonical" old-fashioned vacua are in the
middle of the picture, and the others are related to them. Try it! ;-)
The reason for this gedanken experiment is that I think that there are so
many unknowns in this global picture of string theory and its low-SUSY
vacua and cosmology, that a mild bias can make you lead to very different
conclusions. Allan Adams was explaining me that a specific example of a
Calabi-Yau space with the properties that you need has not been found even
though it is expected that many of them exist; some papers indicate that
some ways of decay might have been overlooked. I also keep on thinking
that non-generic things must be generically unstable because of a large
number of decay channels. In other words, the landscape has morally a
"center" and everything tends to decay to these most natural and
fundamental vacua.
The E8 x E8 heterotic string on Calabi-Yau, to list the conventional
old-fashioned class of vacua (even though I like some new ones, too),
seems to have essentially all necessary features to describe the known
physics properly, starting from a very predictive framework. In my optics,
these vacua are still sort of "canonical" - the biggest achievements of
superstring phenomenology - and they are the most constraining ones among
all the pictures that have been studied.
I also have a feeling that the most important reason why the theorists
started to construct all these "less canonical" examples with a plenty of
fluxes forming the landscape - a landscape of models where the
quantitative details of the model building (GUT etc.) become less
important - is that they *want* to have a large number of vacua, as a way
to solve a single mystery of a single number (the cosmological constant),
and therefore they selectively pick the arguments that are compatible with
this large number of vacua. It is a purpose-driven enterprise.
If you asked someone in the 80s whether there were fluxes in the
Calabi-Yau spaces, they would not know. If you explained them the
superpotential coming from the fluxes, they would like it as a way to
stabilize the moduli, and they would guess that the fluxes are of order
one and the number of models is still rather small. It seems to me that
the main reason why we say that the landscape is large is that we have
been brainwashed, for a couple of years, by these anthropic models. And
these models were studied because we had nothing better to study on the
phenomenological front because the cosmological constant is now the only
known number whose values significantly disagrees with the theories we
know.
In my opinion, the landscape models are less scientifically attractive
because they explain less of known observations or properties of Nature,
and the fact that 2004 is bigger than 1986 does not seem as a sufficient
justification of the statement that they are more sophisticated than the
things studied in the 1980s. They are based on a large number of insights
from the 1990s; they combine them in various ways - there are millions of
ways how to combine these insights to advocate different pictures. But
they are actually less constraining than physics in the 1980s has been.
I will probably have to apologize in advance, :-) but if someone
calculates the top quark mass (from its Yukawa coupling), I still think
that it is a more scientific result than calculating the order of
magnitude of the number of Universes that no one will ever see. It is a
more interesting result, even if this quark mass is calculated decades
before the anthropic calculation. Until someone will be able to make
quantitative predictions of anything based on these landscape ideas, I
will view these ideas as vague ones. The fact that they combine, in a
slightly postmodern way, a lot of insights from the last decade, makes the
situation even worse in my opinion.
Most of the ideas from the 2nd superstring revolution will be viewed as
parts of the structure of the big picture of string theory, and most of
them will never be directly relevant to the experimental testing. From an
experimental point of view, most of them will be irrelevant; this is what
I am convinced about. If you use a large number of such ideas to make a
calculation, it makes the calculation *less* robust, not more robust.
Would you agree with this conclusion?
> While I consider it completely obvious that string theory has many vacua
> and that dS models should exist within string theory, the KKLT paper was
> written in an environment (contrary to what Wolfgang seems to imply) where
> some of these facts were (and are) under active debate.
The idea that dS cannot exist in any sort of string theory, to quote a
very concrete example, is just an artifact of a very specific debate of a
very small number of people in California and on the East Coast, and one
should not be surprised if the dissent against this very limited viewpoint
is not appreciated too much by people from Europe. ;-) The idea has always
been that string theory can predict positive cosmological constant, by
stabilizing the potential at a small positive value, and low energy
effective field theory can be derived from such string theory, even if it
is in de Sitter space. The existence or non-existence of the S-matrix in
de Sitter space is a technicality unrelated to string theory. If de Sitter
does not admit an S-matrix, does it mean that we can rule out that we live
in dS by pure thought? I don't think so. This observation just limits the
accuracy with which dS physics can be predicted from any theory. But there
can still be a rigorous framework in string theory that contains some
objects and that, indeed, agrees with the non-existence of the de Sitter
S-matrix.
I agree with Wolfgang that the idea that the number of vacua is large is
neither new nor attractive nor convincing, and I think that the recent
arguments are based on a too large number of untested assumptions.
> As far as the science goes, it seems to me the clearest directions for
> work involve either finding examples where more pieces of the
> superpotential are exactly calculable (about which I have some ideas ...
It's great if things are calculable, and these tools will of course
survive even if the landscape won't. Of course, the only reliable way to
escape from the universal and mostly unpredictable anthropic quagmire is
to offer a conventional scientific explanation of some yet-unexplained
facts and numbers. But we will have to wait - or perhaps even think - for
a long time. ;-)
Best wishes
Lubos
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Wolfgang Lerche
> While I consider it completely obvious that string theory has many vacua
> and that dS models should exist within string theory, the KKLT paper was
> written in an environment (contrary to what Wolfgang seems to imply) where
> some of these facts were (and are) under active debate.
In this I am on your side and opposite to Lubos'. As said, what
irritates me is that the impression is being created (and I was not
talking about your paper), that the fact that there are very many
string vacua, would be a new result. In particular, when reading
certain recent interviews, I see some sort of "paradigm shift" being
celebrated, some apparently revolutionary novel, anthropic way of
thinking about string theory. But we all know since almost two
decades that there exist abundantly many string vacua which seem
perfectly fine, and anthropic ideas have been voiced by many people
before.
> I think it is fair to say that these points involving control over
> moduli potentials (and hence countings of models with no moduli,
> as opposed to constructions based on worldsheet CFT which are parts
> of moduli spaces that will be lifted) are things that make the
> discussion today more sophisticated than the one that could have
> occurred in the mid 1980s.
Surely it is - but the problem of vacuum selection exists for the
whole set of vacua, including stable ones with extended
supersymmetry and in higher dimensions, independent of any lifting of
moduli. Thus the question whether or not to invoke the anthropic
principle arises already at the level of these old CFT constructions,
even without including flux and/or brane backgrounds.
For me and others, the paradigm shift happened in the mid-80's, and
not now. Recall that those (by today's standards indeed quite
simple) 4d string constructions based on worldsheet CFT were done
in an environment where the uniqueness of the heterotic string was
praised, and more than a few colleagues seemed to expect the standard
model to pop out from some compactification at any minute. That
then instead a "landscape" of 10^(some number with lots of digits)
vacua popped out, came indeed as quite as a surprise; even if most
of them may not be stable at the end, there remain plenty of stable
ones among them.
As for my other brief remark, I alluded not to the content of the
KKLT paper but to a certain style of doing things ;-) To be sure,
this paper is a great piece of work, and I certainly do recognize
its achievements.
Shamit Kachru
OK well to avoid what I consider mostly unscientific discussion (I don't
particularly learn from tirades for or against the anthropic principle), I
will limit this to my last reply.
I find that this discussion (not only this one, but most chat-level
discussions of KKLT and related papers) confuses and conflates three
issues. I will separate them so that they can be discussed independently,
which to me is the right way to discuss them:
1) Can we characterize the space of string vacua (is it small and
constrained, large and unimaginably diverse; are there points that
look like our world?).
2) Does string theory have dS vacua? If so, can we use details of
their properties to illuminate mysteries about dS quantum gravity?
3) Do we think string theory offers a "natural" explanation of the
small CC?
On point 1):
I think since the mid 1980s there has been a lot of progress. I think
we now have a much better idea about how to compute moduli potentials;
I think this will improve again by an order of magnitude in the next
5-10 years, as we learn to combine information from the topological
A and B models to get full superpotentials. (I have some ideas about
this, not ready for even this level of discussion yet).
We also have a much better idea about possible decay channels; beyond the
Dine-Seiberg instabilities (rolling or tunneling to large radius or zero
coupling), we now understand how D-brane and NS-brane domain walls can
allow for instance different flux vacua to tunnel amongst one another as
used in papers that I and many others have written.
Given this, there is (in my mind) a good chance that we already know the
most significant contributions to effective potentials, and to decay
rates, for a large class of vacua (maybe there are other classes we know
less about; that won't matter for my purposes). And therefore, with hard
work and improved estimates, we can probably FIGURE OUT whether they are
long lived compared to the string time. This was checked for some decay
channels in the KKLT paper (and in an earlier paper I wrote with Pearson
and Verlinde), and in slightly different constructions was tested by a
UCSB paper by Frey et al.
The nice thing about this circle of questions it that with no
philosophical preconceptions, it is amenable to precise answers. For
instance the Douglas conjecture (refining Bousso-Polchinski) for the
number of no-scale flux vacua; or conjectures about where vacua lie on the
moduli space; are all precise statements to test. If these statements are
tested and turn out to be true (which is going to happen shortly), they
provide some evidence that we know what we are talking about with this
class of models. The next important step will be to go beyond such
no-scale approximations and find similarly calculable classes where all
moduli are gone; but again this seems clearly amenable to technical
progress to me, mostly because a small fraction of the resulting models
(but a large absolute number) will lie at large enough radius for
asymptotic expansions to make sense, and because non-renormalization
theorems allow good computations of superpotentials. The former fact
relies crucially on the large number of no-scale vacua; the tails of the
no-scale distribution will have the right properties to allow
stabilization of further moduli at relatively large radius.
Now, these facts about really calculable things (NOT assumptions) are what
go into KKLT until the point where one stabilizes the last modulus; it is
there that the genericity arguments become crucial. But as we can discuss
when I am at Harvard, the idea that this genericity argument is wrong
would be completely shocking. From the low energy point of view it would
be unprecedented in string theory; from the high energy point of view it
would require all kinds of miracles, which may happen in tiny special
classes of models, but certainly not in general CY models (I would be
happy to talk to Allan about why I say this; I don't think we need a CY
with any particularly special properties, though this doesn't seem to be
understood by some people; the genericity arguments work for any CY).
And as our ability to compute improves, the last genericity argument will
(I am quite confident) be confirmed. At the current time, at the level of
no-scale counting, the huge degeneracy is inarguable, it is simply a
mathematical fact about properties of solutions to certain differential
equations (periods) on Calabi-Yau spaces.
You can always say then: `` I don't like large numbers of vacua because
they can lead to anthropic thinking; so I believe there is a subtle
inconsistency we haven't uncovered yet. '' Of course you could also say
this about string theory in general if you don't like it, or about quantum
mechanics (which however has the large bonus of experimental confirmations
:)). So at that level I find the debate meaningless. Once the technical
understanding is shored up in the ways I mention above (which will require
lots of work but is clearly going to be done in the next several years
just due to ongoing works by various people), I think the nail will be in
the coffin for ``monovacuists." This doesn't mean that one will have to
think anthropically. They are separate issues. It could be that the
degeneracy of vacua with certain properties, is completely dominated by
those which have those properties for reasons of beautiful symmetry (e.g.
I bet all vacua with vanishing CC will be exactly supersymmetric).
It is always possible that cosmology will add a new unique selection
principle; again, I have no reason to think this is true or false.
So exhibiting lots of roughly static vacua would still leave logical
possibilities for a unique outcome. This would be great.
And, having a large number of vacua does NOT mean one gives up on
predicting things. Au contraire, the whole point of this exercise is to
correctly survey whats out there, to figure out what we can predict and
how we should go about doing it. It seems to me hard to argue that this
shouldn't be attempted, though of course there may be other equally or
more interesting things to do at any given time in our field (and
healthily, different people will choose to do different things).
On point 2):
I think debating issues about holography or conceptual issues of quantum
gravity in dS space, without precise examples, is much less fruitful than
trying to learn from examples. While the existing proposed examples
(really scenarios) of dS space are hideous Rube-Goldberg type contraptions
(to quote from my colleague), they are nevertheless useful in some ways.
For instance the same KKLT paper helped relax some worries about
recurrence times in dS space, which bedeviled some attempts at dS
holography; and I have colleagues who see promising approaches to
explaining the degrees of freedom of dS space (the entropy) by using the
ingredients that go into flux constructions. But anyway, whatever the
final decisive picture of dS quantum gravity that emerges is, having ever
improving and more controllable examples can only enrich our
understanding.
On point 3):
The best positive argument here would be examples where string theory does
do this miraculously! We don't have any. I have certainly spent much of
my time trying to do this as people who know me can verify. I would hope
that eventually someone would find a method; this would not contradict
anything I said in 1) or 2).
Absent that, the anthropic reasoning or whatever you want to call it does
offer an explanation: the standard one in science, of correcting your
analysis of data for the observing device. I don't personally find this
very interesting or rich, but I have very bright colleagues who do.
But here I have to add something slightly personal and historical: Anyone
who thinks the authors of KKLT set out to write a paper proving the
existence of a discretuum to justify anthropic reasoning, is insane. A
simple glance at SPIRES will show that I was working on flux vacua for
several years, as computable models where the rather severe moduli
problems of older (and less generic) constructions could be solved. So was
Trivedi. And Andrei and Renata were working on making cosmological
backgrounds in string theory. So what happened of course is that we
started talking and put our interests together. My clear motivation from
2001 for studying flux backgrounds was that I think older constructions
face really severe challenges from moduli problems. It then so happened
that the flux vacua, which can help alleviate these problems, also give
rise to this huge degeneracy.
The huge degeneracy was important, not because it allows anthropic
reasoning, but because it gives one a technical tool; it gives rise to an
argument (amenable to detailed study) that some of the vacua will come
with small expansion parameters (what we called $W_0$ in the paper).
While the fraction with small $W_0$ will be small, the absolute number
will be large, so with any rudimentary knowledge of distributions you will
be able to convince yourself that you aren't talking about the empty set.
OK sorry for the long-winded reply. As I said I promise it will be my
last; I think all three of the questions above are quite interesting but
my focus has mostly been on 1), and anyway both 1) and 2) clearly give
rise to problems that are amenable to technical progress. So our time
would be better spent attacking the real questions instead of debating
philosophy.
Best regards,
Shamit
Joe Polchinski
wrote in message news:
> Well, what I find irritating is that these ideas are out since the
> mid-80's; in one paper on 4d string constructions a crude estimate
> of the minimal number of string vacua was made, to the order 10^1500;
I'd like to get the reference on this, I came across this number
recently in Andre Linde's book from around 1990; he got the number
from Mike Duff, but I guess that Mike got it somewhere else.
> this work had been ignored (because it didn't fit into the philosophy
> at the time) by the same people who now re-"invent" the landscape,
> appear in journals in this context and even seem to write books
> about it. There had always been proponents of this idea, which is
> not new by any means. Surely the number of 4d string constructions
> has vastly increased since that time, and they have been become much
> more sophisticated, but that's only a quantitative change; the whole
> discussion could (and in fact should) have been taken place in
> 1986/87.
> The main thing what has changed since then is the mind
> of certain people, and what you now see is the Stanford propaganda
> machine working at its fullest.
I would say that the biggest thing that has changed is the
experimental data. If the CC had come out zero, we would still be
looking for a symmetry explanation. The anthropic explanation would
be pretty close to falsified: if the vacuum energy is much smaller
than other energies, it does not affect the cosmological evolution and
so the anthropic principle can't act. The fact that it is comparable
to and slightly larger than the other energies (right now) is an
incredible cosmic coincidence, which needs to be explained, and was
predicted by Weinberg. For fifteen years I have watched the mounting
evidence for a CC (remember the age problem?) and hoped that it would
go away because I didn't want the anthropic argument to work. It
didn't go away.
Further I do not recall anyone ever in this context suggesting that
one would get a spectrum of CC's, which is the essential feature of
the landscape. Also the fact that most/all of these vacua are
unstable, which is needed to populate the landscape. Nor the
connection with the anthropic principle. Certainly not in print, but
not even in private.* For good reason, there has always been a strong
self-censorship among string theorists with regard to the anthropic
principle ... in our paper Raphael had to cajole me to include it,
even though I was aware of its inevitability. In fact in string
theory there is a cult of `monovacuism,' whose prophet resides in New
Jersey (or possibly in the office below mine), to the effect that some
magic principle will pick out a single vacuum, namely ours. I would
like this to be true, but scientists are supposed to be immune to
believing something just because it makes them happy.
*A striking exception is a 1984 paper of Andrei Sakharov, which gets
it all right.
Lubos Motl
thank you for your continuing inflow of interesting ideas and knowledge.
Let me also try to answer these well-posed questions differently.
> 1) Can we characterize the space of string vacua (is it small and
> constrained, large and unimaginably diverse; are there points that
> look like our world?).
No doubt, there has been a lot of progress connected with this question.
But we don't quite to seem to agree about the sign of the direction
where the progress led.
The Second Superstring Revolution is first of all a Duality Revolution.
What used to be five versions of the theory based on the stringy idea
became six :-) different vacua in the moduli space of a single theory. I
am rather sure that you would agree with the previous sentence.
Second, "different theories" associated with different Calabi-Yau spaces
have been connected by the critical transitions. The idea that the number
of vacua/theories was large has been with us from the very beginning. A
short time after Andy Strominger found the quintic in the library - which
they could believe was the only (Calabi-Yau) solution needed to complete
the picture of Candelas+Horowitz+Strominger+Witten and define a theory of
everything - thousands of manifolds and vacua have been found. In the
1980s, they would not be thinking in terms of fluxes, but they would
certainly tell you a lot of different Calabi-Yaus and orbifolds with
Wilson lines and asymmetric orbifolds etc. that seemed to suggest that the
number of vacua (called "theories" at that time, or at least "models") was
large. These discrete choices are not that popular anymore; in my opinion
it is mostly because of a new way of fashion.
Everyone seems to talk about the geometrical vacua equipped with fluxes
etc. mostly because he or she sees that many other people talk about it.
Almost no one would talk about the free fermionic heterotic models because
they are not popular anymore; still, they were more predictive about the
properties of the elementary particles etc.
OK, let me return to the role of the duality revolution. A big victory of
the 1990s is the insight that all these choices (like the topologies of
the Calabi-Yaus or the 5 versions in 10 dimensions) seem to be connected.
Various options are totally equivalent to one another, and others are
connected (often on the moduli space) and allow you to go from one to the
other; others can be connected off-shell and via tunnelling etc. The BPS
and other checks of all these relations are nontrivial and convincing. As
far as we work with stable supersymmetric configurations, I believe that
there is little space for differences in the interpretation.
There has also been a progress in the moduli stabilization problem and
many contributions to the (super)potential have been precisely isolated,
both the perturbative ones as well as the non-pertubative ones as well as
those related to the fluxes and other objects. OK, you believe that you
will know essentially the whole potential relevant for anything in string
theory soon; I am afraid that we don't even know the right question.
String theory was extended to contain a lot of new ideas and objects, and
that - of course - allowed the people to apply their imagination in a
plenty of different ways. The number of conceivable string vacua increased
again, and there is even a huge dimension of the space of ways in which we
can extend the number. Today we just have a slightly different way to
encode this possibly large number. The number of asymmetric orbifolds or
free fermionic heterotic models or whatever else was hot in the late 1980s
is not that popular anymore because these things sounded too perturbative.
But honestly, can you exclude that a generic background is a non-geometric
vacuum generalizing the asymmetric orbifolds in a M-theoretical way? What
do you think about the nonperturbative fate of all these seemingly
perturbatively consistent models? Can you rule out the possibility that
there is a subtle discrete anomaly that kills a whole class of seemingly
generic backgrounds, and defines a very different class? Can you prove
that your huge families of vacua are compatible with *some* cosmology
according to the full rules of quantum cosmology? All these tools and
possibilities - going both ways - exist and they have always existed.
There have always been many ways to generate a huge number of backgrounds,
and there have always been many possibilities that a majority of them is
inconsistent, equivalent, or unstable, or perhaps, that all of them are
distinct and they do exist.
Because the set of all vacua that we should understand has increased
significantly, and our tools to organize all these things only increased
by a comparable amount, we can't really be more certain about the question
"how many vacua there are?" than what we've been decades ago.
Don't get me wrong. Your paper(s) about it as well-written as one can
imagine assuming the current state of our knowledge. But that's a
different criterion than the scientific robustness of the arguments. I
guess that you would agree that the landscape is not giving, so far,
testable predictions, not even qualitative ones, not even quantitative
theoretical ones that can be independently checked (in theory). The number
of consistency checks of these anthropic ideas is negligible, and the
number of observational/experimental tests is zero, and these models just
don't seem to confirm the properties of the world around.
> 2) Does string theory have dS vacua? If so, can we use details of
> their properties to illuminate mysteries about dS quantum gravity?
I think that the amount of solid insights about de Sitter space and its
"axiomatic" properties, that were revealed within string theory, is -
despite the hundreds of papers - infinitesimal, and it seems that we would
agree about this point. ;-) I never believed that there were interesting
things waiting to be found about the Poincare recurrence; S-matrix in de
Sitter space; finiteness of the Hilbert space etc. I also agree that it
is better to work with the explicit backgrounds/examples where the
questions can be sharper. But these examples, I think, should not be too
contrived because then the conclusions are not robust. A background that
uses all possible types of branes, warping and geometrical effects is a
contrived background.
> 3) Do we think string theory offers a "natural" explanation of the
> small CC?
It seems to me that it is not realistic that this question appears as #3
because it was actually more or less the primary question that made the
people work on all these 3 points and cosmology in string theory. The
experimental evidence for a positive CC was viewed as a reason to start to
work on these issues in string theory - although there was a very small
chance that something reliable would emerge from it given our state of
understanding of string theory (and quantum cosmology). Because people
have written hundreds of papers that have not led virtually anywhere, and
some people are afraid to admit it, many are starting to fool themselves
and believe that they have evidence for all these incarnations of the
anthropic reasoning because the anthropic solutions are, so far, the only
ones that have been found - because the anthropic solutions can *always*
be found. They are generic and they always allow their daughter ideas to
live for a while. ;-)
There is, of course, a legitimate possibility that the number of vacua is
very large. But even if it is a possibility, one should still insist on
the scientific ways of deciding whether an argument or a theory is robust.
If a calculation does not give any testable numbers, does not confirm any
known observations and has no consistency checks, and it is based on
extrapolation of our incomplete knowledge to a totally untested regime,
one should remain cautious, I think.
Let me say one more trivial answer to the question "Does string theory
have a natural explanation of the small CC?" With some tolerance, the
answer is Yes. It can easily explain why the CC is zero in vacua with a
sufficient SUSY. Although this is not enough for a realistic model - with
broken SUSY - it is still a good moral example showing that such
explanations giving us exactly what we need *are* there, and they might be
eventually found even for the troubling number called the CC. And because
we have not obtained the correct value for a single number (CC), it does
not mean that we should give up all predictions of many properties of the
elementary particles, and so on, that result from the "canonical", simple
enough models.
> But here I have to add something slightly personal and historical: Anyone
> who thinks the authors of KKLT set out to write a paper proving the
> existence of a discretuum to justify anthropic reasoning, is insane. A
> simple glance at SPIRES will show that I was working on flux vacua for
> several years, as computable models where the rather severe moduli
> problems of older (and less generic) constructions could be solved.
I did not quite understand your argument. Is not it evidence for the
original (insane) statement? ;-) Who else should write a paper defending
the importance - or even genericity (in the "anthropic" ensemble) - of a
class of vacuum, than the person who had been working on it for years? Is
not it logical? ;-) Should not we at least admit the possibility that the
flux vacua are not generic or interesting vacua that most people should
study? In the 1980s, people would define the ensemble as different
orbifolds of Calabi-Yau's with various Wilson lines, today many would say
that a generic vacuum is a flux compactification. But do you think that
now we really know the measure? Do you have evidence that the new favorite
"generic" model won't change again in 2008?
> The nice thing about this circle of questions it that with no
> philosophical preconceptions, it is amenable to precise answers. For
> instance the Douglas conjecture (refining Bousso-Polchinski) for the
> number of no-scale flux vacua; or conjectures about where vacua lie on the
> moduli space; are all precise statements to test.
Is the meaning of the word "moduli space" exact in this sentence? Do you
mean only the exact moduli spaces? Or do you think that we know how to
generalize this concept beyond the exact moduli spaces? If we study vacua
with potentials (and SUSY breaking) and it should be more than a
perturbative expansion around the higher-SUSY backgrounds, should not you
include all scalar fields to your scalar configuration space? Will you
include the whole infinite tower of scalars from perturbative strings, for
example? Or what exactly justifies the truncation?
> Now, these facts about really calculable things (NOT assumptions) are what
> go into KKLT until the point where one stabilizes the last modulus; it is
> there that the genericity arguments become crucial.
Is it OK to say that genericity arguments for vacua are always assuming
the anthropic framework? Is not it better to look for the correct theory
and correct vacuum instead of the generic ones in some contrived ensemble? :-)
> But as we can discuss when I am at Harvard, the idea that this
> genericity argument is wrong would be completely shocking. From the
> low energy point of view it would be unprecedented in string theory;
> from the high energy point of view it would require all kinds of
> miracles,
Most of the nice things about string theory involve facts that look like
miracles, and this is exactly what makes them convincing and nontrivial,
once we check that they are true. This is exactly what I am missing in the
anthropic picture; there does not seem to be anything nontrivial going on,
no "miracles". This anthropic picture is always guaranteed to work. It
never works too well, but it always works sufficiently for one to say that
it is essentially OK. Therefore it is a virus that kills people's brains,
as David Gross says.
> which may happen in tiny special classes of models, but certainly not
> in general CY models (I would be happy to talk to Allan about why I
> say this; I don't think we need a CY with any particularly special
> properties, though this doesn't seem to be understood by some people;
> the genericity arguments work for any CY).
It might be much more efficient and fun to discuss it in real life.
> You can always say then: ``I don't like large numbers of vacua because
> they can lead to anthropic thinking; so I believe there is a subtle
> inconsistency we haven't uncovered yet. ''
Right. As soon as someone proposes a different model that will not agree
with some of your statements, but that will give more concrete,
non-anthropic, and perhaps even quantitative predictions, such a model
will be immediately scientifically preferred, and even the task to find
the exact problem with KKLT would become secondary.
> Of course you could also say this about string theory in general if
> you don't like it, or about quantum mechanics (which however has the
> large bonus of experimental confirmations :)).
Of course that you realize that I will only say it about the anthropic
variations of these theories. ;-) There is a big difference between these
three groups of ideas. Quantum mechanics has experimental confirmations,
and "the" nice, more or less "unique" string theory has a lot of
impressive internal consistency and uniqueness checks. What comparable
arguments are underlying the anthropic version of string theory?
> So at that level I find the debate meaningless. Once the technical
> understanding is shored up in the ways I mention above (which will require
> lots of work but is clearly going to be done in the next several years
> just due to ongoing works by various people), I think the nail will be in
> the coffin for ``monovacuists."
Well, I think that the nail will be *always* in the coffin for
"monovacuists" because these are the people who will have the difficult
task to find the correct and predictive explanation. :-) An anthropic
explanation can survive for some time, but of course it only survives
until a better explanation appears.
By the way, let me quote Glashow, but restrict his statements to the
"anthropic string theory" only. I was brought up to believe, and I still
believe, that physics is an experimental science. The anthropic framework
can never be ruled out by any experiment or observation. This theory is
safe. Permanently safe. Is it physics, or philosophy? :-) I ask you!
What I want to say is that string theory itself, to become very generally
believable and accepted, will have to make some successful predictions
about the reality, and the anthropic direction so far seems to make it
less likely. I only believe that string theory is a serious direction in
science because it is able to predict that gravity, other forces and
particles - that exist in the real Universe - appear from a unified
picture and it can explain some of their properties. I don't see such a
justification of anthropic string theory, so far, and therefore it seems
more plausible to assume that something important about SUSY breaking or
anything like that is just purely understood, and the new arguments
suggesting that string theory is much less predictive are not quite
correct. The reduced predictivity certainly goes against the direction
defined by most of the discoveries in string theory that I consider
encouraging; in other words, such an anthropic picture makes string theory
as such less appealing.
> This doesn't mean that one will have to think anthropically. They are
> separate issues. It could be that the degeneracy of vacua with
> certain properties, is completely dominated by those which have those
> properties for reasons of beautiful symmetry (e.g. I bet all vacua
> with vanishing CC will be exactly supersymmetric).
Sure, there can be organizing principles even inside a discretuum.
> It is always possible that cosmology will add a new unique selection
> principle; again, I have no reason to think this is true or false.
> So exhibiting lots of roughly static vacua would still leave logical
> possibilities for a unique outcome. This would be great.
Right.
> And, having a large number of vacua does NOT mean one gives up on
> predicting things. Au contraire, the whole point of this exercise is to
> correctly survey whats out there,
But do you really believe that we know "what's out there?" Don't you have
the feeling that this research of these specific classes of vacua is a
random shooting, and the probability that this is the relevant class is as
large as the probability that we should find the right free fermionic
heterotic asymmetric orbifold?
> The huge degeneracy was important, not because it allows anthropic
> reasoning, but because it gives one a technical tool; it gives rise to an
> argument (amenable to detailed study) that some of the vacua will come
> with small expansion parameters (what we called $W_0$ in the paper).
Well, you needed sigma>>1, which is a<<1, which is related to a large
value of the flux etc. Nevertheless I don't think that your argument is a
scientific argument supporting the assumption, and in my opinion your
paragraph above is a great example how an anthropic publication selection
works and leads to unjustified conclusions.
You say that the degeneracy and fluxes must be large, because *you* need a
large value of sigma because then (you think that) you know how to
calculate in a controllable fashion. But I would like to tell you my
opinion that Nature does not care whether *you* can calculate. Even though
you can calculate many things, my guess is that Nature prefers (either by
genericity, or by more well-defined rules) vacua where many important
things are of order one, strongly coupled, and therefore those which you
*can't* calculate, and in fact, no one else today can calculate them
either.
You are *assuming* that Nature must behave like the vacua in the regime
which you *can* calculate (at least that's what many people think), and
then you are looking for a self-consistent picture based on this
assumption. Even if these vacua exist, I just feel that they cannot be
relevant because in any reasonable parameterization of the vacua, they
would be labeled by a very large integer, and therefore they are unnatural
in some sense and cosmology will disfavor them.
Imagine that a Planck time after the Big Bang, the Universe effectively
jumps between all known vacua, according to some distribution. I just
think that these "generic" vacua with large values of the integers
labeling them will be highly suppressed, and even a random process would
end up in one of the "special" vacua - one outside your "generic"
classes. That's an issue of the choice of the measure (probability
distribution) for the word "generic", and treating the probability to be
equal for each vacuum seems like a very naive measure. Even if this way of
"genericity" thinking is relevant, the correct measure - determining the
meaning of the word "generic" - is determined by cosmology, and I would
bet that it will disfavor the vacua that are "too far", such as the
generic discretuum flux vacua.
All the best
Lubos
Peter Woit
> And, having a large number of vacua does NOT mean one gives up on
> predicting things. Au contraire, the whole point of this exercise is to
> correctly survey whats out there, to figure out what we can predict and
> how we should go about doing it.
If there is an astronomically large number of string theory vacua and
cosmological constant cannot be predicted, can you suggest what is
the most likely physical quantity that will be predicted by string
theory and give a plausible guess for what kind of calculation will
lead to this prediction?
Peter Woit
> In fact in string theory there is a cult of `monovacuism,' whose
> prophet resides in New Jersey (or possibly in the office below mine),
> to the effect that some magic principle will pick out a single vacuum,
> namely ours. I would like this to be true, but scientists are
> supposed to be immune to believing something just because it makes
> them happy.
You're accusing the "univac" proponents of wishful thinking, but what
specific scientific reason do you have for believing that in the
"multivac" picture one will be able to predict anything at all about
physics?
Wolfgang Lerche
> I'd like to get the reference on this, I came across this number
> recently in Andre Linde's book from around 1990; he got the number
> from Mike Duff, but I guess that Mike got it somewhere else.
We used to go to lunch with Mike, so I am not surprised ...
this number is on p33 of our paper
"Chiral four-dimensional heterotic strings from selfdual lattices",
with Lust and Schellekens, Nucl.Phys.B287:477,1987. A link to the
preprint is here: http://wwwth.cern.ch/~lerche/papers/4dhetstrings.pdf
At any rate, these are only very crude estimates, not to be taken too
seriously. But my point is that already with these crude data, one
is lead to ponder about the anthropic principle. And in fact I always
found this an "attractive" (read: perhaps unavoidable) idea, despite
I seem to have created here the impression to the opposite (perhaps
by a bit of provocative writing ... what I was trying to say is
that the very idea of a landscape is not new, as I know from
discussions with many colleagues over the years, and therefore it
need not be celebrated as such).
> that some
> magic principle will pick out a single vacuum, namely ours. I would
> like this to be true, but scientists are supposed to be immune to
> believing something just because it makes them happy.
I absolutely share your point of view !
Joe Polchinski
> You're accusing the "univac" proponents of wishful thinking, but what
> specific scientific reason do you have for believing that in the
> "multivac" picture one will be able to predict anything at all about
> physics?
I do not see the connection between the first half of the question, before
the comma, and the second half, but I do believe that both halves were
already addressed in my post.
Regarding the second half, Sakharov/1984-Weinberg/1989 predicted a
cosmological constant, and it has been seen. This `specific scientific
reason' was precisely the point of my post, and it counts as a pretty
strong argument given that every other approach (and _many_ have been
tried) has failed badly. (You could add in w = - 1, that is a
cosmological constant rather than quintessence, as a second prediction).
Regarding the first half, wishful thinking, I spent ten years wishing that
the Hubble constant would come down to 50, because then the cosmological
constant and anthropic principle would go away, and we would live in a
beautiful universe. But it didn't come down to 50, the cosmological
constant is here, and we live in a universe for which --- independent of
string theory --- the multiverse is the only existing theory that predicts
a value anywhere near that which is observed. The fact that string theory
provides such a spectrum of universes is therefore an argument in its
favor. I believe that most string theorists (and others) were unaware of
what was at stake with the Hubble constant (and other early signs of a CC)
and view the sudden discussion of the anthropic principle as some bizarre
fad, but what has been described by David Gross as a `conversion' on my
part is not that at all: my theoretical perspective has not changed, but
the observations have just told us what kind of universe we live in.
Regarding future predictions, which may be statistical in nature, we have
much to learn and it is too early to say. Indeed, Banks, Dine and
Gorbatov in hep-th/0309170 have given strong arguments that the anthropic
principle is already falsified (even while David Gross tell me that it is
not falsifiable, you can't win in this business). I refer specifically to
their arguments about the baryon lifetime and strong CP violation.
Resolving this issue will take time, and involves many different aspects
of physics, but will likely in the end either leave us with a more
predictive understanding or with the conclusion that the idea is wrong.
Finishing on an optimistic note: there are possibilities like black holes
at LHC and (my pet) cosmic F and D strings, which are not `predictions' of
string theory in the sense that they are realized only in a subset of
string vacua, but if seen are spectacular signatures. As we understand
the theory better we may identify more such `smoking guns, and eventually
see one.
p.s. This was the first time I have posted to such a board, and as I
feared it is a tremendous time-sink --- I just spent my lunch hour
interacting with my keyboard instead of my colleagues. So my apologize if
I am unable to address future responses.
Peter Woit
this posting - not because he has nothing to say, but because he has more
interesting and important things to do. LM]
Joe Polchinski wrote:
> Peter Woit wrote:
>> You're accusing the "univac" proponents of wishful thinking, but what
>> specific scientific reason do you have for believing that in the
>> "multivac" picture one will be able to predict anything at all about
>> physics?
>
> I do not see the connection between the first half of the question, before
> the comma, and the second half, but I do believe that both halves were
> already addressed in my post.
The wishful thinking of the "univac" proponents has always been that
a more or less unique vacuum state could be identified that would allow
predictions about physics to be made. As far as I can tell (I'm hoping
someone better informed will correct me if I'm wrong), the hope that
the "multiverse" point of view will lead to predictions about physics is
also wishful thinking.
I'm using "prediction" in the historically conventional sense of the term:
using new theoretical ideas to make precise calculations of observable
quantities. The multiverse argument about the cosmological constant is
not really a prediction, it is an argument that purports to explain why it
is impossible to make a prediction (too many vacua, too little
understanding of transitions between them, no understanding of initial
state). The range of values it "predicts" for the cosmological constant
is exactly the range I "predict" when I throw up my hands and say I have
no idea at all what determines it.
Will proponents of the "multiverse" really concede that the idea has been
falsified if it becomes clear that too much baryon number nonconservation
and strong CP violation are generic features of the vacua they are looking
at? Or will they just say that "maybe there are lots of the right kind of
vacua we just haven't looked at yet"?
Arvind Rajaraman
>
> The wishful thinking of the "univac" proponents has always been that
> a more or less unique vacuum state could be identified that would allow
> predictions about physics to be made. As far as I can tell (I'm hoping
> someone better informed will correct me if I'm wrong), the hope that
> the "multiverse" point of view will lead to predictions about physics is
> also wishful thinking.
It depends on how many vacua there are. We may have to give up some
predictivity if there are a lot of vacua, but there will still be
predictions if there are not too many. Even if we have 10^{120} vacua, that
only suffices to explain the CC, and the remaining parameters of the
standard model should be predictable.
> Will proponents of the "multiverse" really concede that the idea has been
> falsified if it becomes clear that too much baryon number nonconservation
> and strong CP violation are generic features of the vacua they are looking
> at?
We are a very long way away from such a point.
Regards,
Arvind.