A coherent survey of the problems in LQG and M theory.

[MathematicalPhysicist]

Is there any survey article that accounts for all the problems that are as of yet to be solved in M theory and LQG?

I mean if I'll have time to dive into this field once. (I don't have a girlfriend and I don't plan to, so maths and physics will do).

 

[tom.stoer]

Regarding LQG Rovelli has a list of open issues in appendix A of his Zakopane paper, but not everybody agrees regarding completeness. Especially consistency, absence of anomalies, quantization ambiguities, Dirac observables, ... are missing.

http://arxiv.org/abs/1102.3660

 

[MathematicalPhysicist]

And for M-theory or F-theory?

Thanks.

 

[mitchell porter]

There are hundreds of open questions in string theory. Pick any paper at random and, if you read it closely, you will probably find an unanswered question. But the ultimate questions of string theory are still: what is the fundamental mathematical form of the theory; and, how do we get the known particles and forces out of it.

A simple-sounding example of a relatively fundamental theoretical question from M-theory is, what is the field theory that describes the low-energy behavior of a stack of M5-branes? In string theory, a stack of N D-branes usually gives rise to a supersymmetric U(N) gauge theory; in M-theory, a stack of M2-branes is described by a Chern-Simons theory with matter, such as the "ABJM" theory; but there isn't a good description for the M5-branes.

Meanwhile, work on "F-theory GUT models" can provide numerous open problems in phenomenology (connecting F-theory to the real world), as they try to construct brane configurations with all the features of the standard model.

If you have video, I suggest watching the summary talks from the annual String and String-Math conferences, to obtain a sense of what people are working on.

 

[tom.stoer]

David Gross collected the main open questions for a Strings conference a couple of years ago; I'll try to find the slides

 

[tom.stoer]

I made some notes based on slides David Gross presented at a string conference; unfortunately I cannot find the slides, so here are the notes:

-----------------------------------------------

WHAT IS THE NATURE OF STRING PERTURBATION THEORY?
Our present understanding of string theory has been restricted to perturbative treatments. Does this perturbation theory converge? Most likely it does not. In that case when does it give a reliable asympototic expansion of physical quantities? How can one go beyond perturbation theory and what is the nature of nonperturbative string dynamics? This question is particularly difficult since we currently lack a useful nonperturbative formulation of the theory.

STRING PHENOMENOLOGY
Here there are many questions that can all be summarized by asking whether one can construct a totally realistic four-dimensional model which is consistent with string theory and agrees with observation?
Great progress, but still not constructed.

WHAT PICKS THE CORRECT VACUUM?
This is one of the great mysteries of the theory which appears, at least when treated perturbatively, to possesses an enormous number of acceptable (stable) vacuum states. Why, for example, don’t we live in ten dimensions? Does the theory possesses a unique vacuum, in which case all dimensionless physical parameters would be calculable or is the vacuum truly degenerate, in which case we would have free parameters? How does the value of the dilaton field get fixed, thereby giving the dilaton a mass? Does the vanishing of the cosmological constant survive the mechanism that lifts the vacuum degeneracy?

The crucial issue is still unresolved: The cosmological Constant

IS THERE A MEASURABLE, QUALITATIVE, DISTINCTIVE PREDICTION OF STRING THEORY?
String theories can, in principle, make many “postdictions” (such as the calculation of the mass ratios of quarks and leptons, Higgs masses and couplings, gauge couplings, etc.). They can also make many new predictions (such as the masses of the supersymmetric partners of the observed particles, new gauge interactions, etc.) These would be sufficient to establish the validity of the theory, however in each case one can imagine (although with some difficulty) conventional field theories coming up with similar pre or post dictions. It would be nice to predict a phenomenon, which would be accessible at observable energies and is uniquely characteristic of string theory.

WHAT IS STRING THEORY?
This is a strange question since we clearly know what string theory is to the extent that we can construct the theory and calculate some of its properties. However our construction of the theory has proceeded in an ad hoc fashion, often producing, for apparently mysterious reasons, structures that appear miraculous. It is evident that we are far from fully understanding the deep symmetries and physical principles that must underlie these theories. It is hoped that the recent efforts to construct covariant second quantized string field theories will shed light on this crucial question.

What is the fundamental formulation of string theory?
Quantum Space of all 2-d field theories
Second Quantized Functionals of loops (SFT)
M-theory . . .
Is string theory a framework, not a theory?
What is missing?

 

[marcus]

Hi Tom, those look like notes from the opening talk at Strings 2009 which David Gross gave in Rome:
http://strings2009.roma2.infn.it/talks/Gross_Strings09.pdf

 

[tom.stoer]

Exactly.

 

[LBloom]

On the topic of problems in LQG, does anybody have good literature or explanation of the problem of getting a flat universe and/or the Einstein equations in the semiclassical limit?

 

[marcus]

http://arxiv.org/pdf/1101.4049v1.pdf

A flat space-time solution does not expand. This paper is about getting a de Sitter solution in the limit (which would be more to the point.)

I guess by getting "a flat universe" you might mean a spatially flat solution. In that case maybe getting the de Sitter case would count as progress, I suppose.
This is all work in progress, just gradually getting closer to full solutions.