Solving thermal QCD using string theory techniques

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My research directions at McGill in the last few years have been along strongly coupled gauge theories, an example being Quantum Chromodynamics (QCD). In particular I have attempted to have some analytical control over these theories. Clearly standard perturbative techniques, like Feynman diagrams, are not useful to analyze these theories because of strong interactions. In the limit where the number of “colors” N is made large, a new development in the field of string theory has shown that there could be a dual gravitational description of these theories wherein all the non-perturbative physics can be analyzed simply using classical supergravity techniques! In the past few years we have been able to develop a model purely using supergravity techniques that mimic large N thermal QCD both at low and high energies. We have been using this model to compute many observable physics of thermal QCD, namely shear viscosity, entropy, QGP phase, confinement and deconfinement dynamics, quarkonium melting etc. These developments are timely no doubt and for the next few years I want to devote my time to develop the picture further and extend this to the color superconductivity phase. The physics of large N thermal QCD and color superconductivity have amazing similarities, and the gravitational description that we have developed here could probably be used to study this further. Additionally, the model that we have developed behave well at high energies too. This is one advantage that I believe is missing in many of the other models proposed in the literature. The high energy behavior of standard QCD is simple: it is an almost free theory. In the large color limit i.e in the large N limit, the high energy behavior is conformal or alternatively, scale-invariant. This is exactly how our model behaves at high energies. In the gravitational dual, the high energy behavior is captured by the regions at large radius and the low energy behavior is captured by the regions at small radius. However the full gravitational dual solution is still not been constructed, and one of my long term aim would be to complete this picture. The exercise is technically challenging, but I believe that with efforts and with the help of my graduate students, we should be able to complete the dual description. Once the dual description is laid out, it will be very interesting to work out analytically the various properties of QCD which were impossible to solve using previous techniques. My second proposal is to work on certain aspects of cosmology that has recently generated some interest. For sometime it was thought that string theory would easily generate de-Sitter type vacua provided certain no-go conditions were violated. A candidate solution was also proposed that took into account various non-perturbative effects that gave us a way at least to study de-Sitter solutions in string theory, although no explicit solutions were constructed. However, recently, certain issues were raised regarding this approach. One of my aim for next year or so would be to resolve this issue. This is a technically challenging exercise as explicit supergravity solutions in string theory that give rise to accelerating universe is very hard to construct. If successful, this would probably be the first non-trivial example of a time-dependent supergravity solution. My third proposal would be to elaborate on the recently proposed gauge/gravity duality in heterotic string theory wherein we gave the gravity dual for a gauge theory whose field theory description was completely mysterious. My aim would be to learn about this theory using our proposed dual. Finally, my fourth proposal would be to extend the newly found conformal Seiberg-Witten type gauge theories using techniques of string theory.