and led by Steve Shenker. We have had many discussions about this topic but I still believe that there are many people (and perhaps readers of this blog) who have interesting ideas that many of us have not heard.
A way to formulate the question is
- What is the most underestimated research direction in current theoretical physics?
It may be that today there also exists a research program that will eventually convince the people that it is the right idea that will allow us a new wave of significant progress. The question is:
- What is it?
Loop quantum gravity
Can it be loop quantum gravity that will join string theory? I've spent hundreds of hours with this kind of idea and did not make much progress. Of course it does not mean that no one else can make more progress than I did. Nevertheless there are many reasons to think that loop quantum gravity is truly incompatible with the most up-to-date ideas about theoretical physics. At the same moment it is important to say that some particular methods could play some role in string theory. If you remember, Thomas Thiemann proposed his "new string theory" in 2004 - which was defined as the representation theory of the so-called Pohlmeyer charges. The Pohlmeyer charges, in their original form, indeed became important in recent string theory developments. For example, you can see a paper by Andrei Mikhailov that identifies the Pohlmeyer charges as the origin of "integrability" of "AdS_5 x S^5". It's a pretty interesting stuff that could help to solve the planar limit of this background. Even such a great insight would probably not be enough to spark the new revolution, I am afraid.
Berkovits and RR-backgrounds
Another proposal what the underestimated research direction could be are the Ramond-Ramond backgrounds. Some people, such as Davide Gaiotto, believe that there is something new about the Ramond-Ramond backgrounds that could shed new light on some conceptual issues of string theory; a great example is the strongly curved AdS space that should be described by a weakly-coupled gauge theory - a regime where the power of the AdS/CFT correspondence has not been exploited too efficiently.
Because the Berkovits pure spinor formalism is currently the only approach that allows one to study arbitrary Ramond-Ramond backgrounds - at least perturbatively - it is also the Berkovits' approach that could help in this kind of progress. Nathan Berkovits is a very smart and powerful guy and his equations seem to fit together. However, at the same moment, it is important to note that there are many reasons why others - including the leaders of the field whose name I will suppress here - believe that reformulating string theory in this new language is just a technicality that will not alter the qualitative shape of our understanding of string theory.
Exceptional groups
It is not hard for me to imagine that the investigation of the exceptional U-duality groups may initiate the next revolution. Although we need to understand pretty complicated backgrounds - involving Calabi-Yau spaces, G_2 manifolds, or complicated orbifolds - to describe the real world - and we don't really know "What string theory on these backgrounds exactly is" - there are much simpler backgrounds that we do not really understand. M-theory on six-torus has a "E_{6(6)}(Z)" U-duality group, everyone believes. How do you derive this fact? What is the generalized geometric framework that underlies these exceptional groups in string theory and makes their appearance manifest? The exceptional groups may simply "be there" and they should be a starting point. This is what people like Hermann Nicolai with his E_{10} or Peter West with his E_{11} believe, much like Ori Ganor and others who have also been very excited with this direction. Can a wave function on these complicated infinite-dimensional group manifolds and their (so far unknown) supergeneralizations define all of string/M-theory or at least its 32-supercharge subsector? I can imagine very well that it is the case. When such a dream would be realized, people would have to generalize the conditions that these group manifolds satisfy in order to find a similar definition for the most general backgrounds - ones that would also include the real world.
The exceptional symmetries are also relevant for the Mysterious Duality, another insight whose importance may be underestimated. When I mentioned the Mysterious Duality, I should also say that it is plausible that we will discover that the worldsheets are not quite fundamental but they are rather target spaces of some other string theory - and this self-generating capability of string theory may even continue indefinitely, or be a subject to some bootstrap self-consistent conditions. I've tried to combine and recombine these ideas for a long time but the current state of affairs remains unconvincing although it is extremely tantalizing.
Expansion of topological strings or matrix models
Topological string theory is a nice subfield of string theory that has very deep connections to mathematics and some connections to the full string theory. There are many interesting equivalences operating in topological string theory, for example the quantum foam as a dual discrete description of geometry. It is plausible that these ideas may be generalized to the full string theory. Actually, after some thinking, I believe that the IKKT model is the closest thing to the quantum foam that you can find in the full string theory. It is not quite discrete because the full string theory has many more degrees of freedom than topological string theory which implies that some discrete structures are replaced by continuous ones.
Also, there are links between topological string theory and the matrix models. While these simple backgrounds of (generalized) string theory may be thought of as toy models that are appealing because many properties are exactly calculable, it is conceivable that one may "extend" them to describe more realistic backgrounds. I personally find it unlikely.
Phenomenological attempts
It is also conceivable that someone - or a group of people - is very close to identifying the correct background of string theory that describes reality, and it is a matter of weeks, months, or years before convincing evidence that their background is the correct one will emerge. Among the promising backgrounds, I would list:
- the weakly coupled or strongly coupled (HoĊava-Witten) heterotic strings with an "E8 x E8" gauge group and an appropriate Calabi-Yau - the most interesting recent example is the Heterotic Standard Model. This is the class of models that gives the most natural explanation of the particle spectrum - namely the fermions being naturally grouped into grand unified families.
- asymmetric orbifolds and free fermionic heterotic models - it is related to the previous item but the Calabi-Yau is replaced by fermionic worldsheet degrees of freedom that are roughly equivalent to a Calabi-Yau near a self-dual radius. While many advantages of the geometric Calabi-Yau backgrounds are preserved, a natural explanation of the number of families (three) may be given in the free fermionic models.
- intersecting brane worlds - type IIA with orientifold planes and D6-branes and matter that lives at the intersections. The most attractive feature of these models, as far as I can say, is that the Yukawa couplings may be naturally hierarchical because they arise from disk worldsheet instantons where the disk is actually a triangle stretched between the three relevant brane intersections.
- M-theory on G_2 holonomy manifolds - many of them may be viewed as the strongly coupled dual of the previous example. Note that the worldsheet instanton from the previous item becomes an M2-brane instanton in M-theory.
- type IIB flux vacua, F-theory on Calabi-Yau four-folds. This is the type of vacua that is the most appropriate one for including warped geometries and Randall-Sundrum ideas. Some people also consider(ed) a large degeneracy of these vacua as another advantage but others disagree(d) and it is reasonable to expect that the importance of the anthropic/statistical approach will start to diminish - after nearly 5 years - because the infinite landscape has just been isolated and it makes any statistical predictions impossible.
Let me list some of them, and your additions will be welcome. Let me start with the conceptual questions, and then continue with the questions that are important for connecting string theory with reality. The most important conceptual question remains "What is string theory?" But let me be a slightly more specific.
- Conformal field theory on the worldsheet describes all expansions of stringy S-matrices that are perturbative in the coupling constant.
- Is there some generalization of the axioms of conformal field theory that allows conformal field as a special, limiting solution, but also offers some other, strongly coupled solutions?
- These extra solutions should include M-theory in 11 dimensions.
- Is there some way to define M-theory in 11 dimensions - a variation of the BFSS matrix model, for example - that has shares some features with perturbative string theory so that a unified definition is possible?
- Is there a rigorous way to describe string theory in a language that makes spacetime locality more manifest? String field theory is an obvious candidate but it has its own problems.
- Is spacetime supersymmetry an inevitable component of consistent string-theoretical backgrounds? If it is so, is it always broken below the Planck scale?
- Can we identify a non-perturbative inconsistency of various "suspicious" backgrounds including supercritical and subcritical string theory and/or the large ensembles of flux vacua?
- Can we isolate predictions of string theory that are not reproducible in field theory? By these predictions we mean things that are possible in field theory but impossible in string theory - for example, a pure N=2 supergravity in d=4 which is Cumrun's favorite example. Can we prove that such low-energy physics can never arise from string theory?
- Can we describe how does the information escape from a black hole once we believe it is not lost? Concerning the black holes, what happens if an observer falls to the black hole? Does GR describe her life correctly? Are there exact observables associated with this doomed observer?
- Can we make general predictions of string theory about the real world that do not depend on the choice of the background?
- Is there a scientific solution of the cosmological constant problem? By the adjective "scientific", I mean a solution that does not require the ideas from the Intelligent Design - or, equivalently, a terribly lucky design - theory.
- Does string theory predict spacetime supersymmetry and if it is so, what is the scale of SUSY breaking? What is the mechanism of its breaking?
- What is the typical size of the additional dimensions? Is it near the naive Planck scale, as the people have been thinking for decades (and reasonably, I think), or is one of the large or warped extra-dimensional scenarios realized?
- What is the correct vacuum of string theory that describes the real world?
- Is it possible to calculate the top quark mass, other masses, and other Standard Model couplings from string theory, and predict physics at higher energies?
- Does string theory tell us something about the initial conditions of the Universe - something along the Hartle-Hawking lines? Beyond the supersymmetric subsector, this may require the "local" formulation of string theory mentioned above.
- Does string theory predict additional objects - or corrections to cosmological perturbations - that are testable? How many types of cosmic strings do we have?
