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(Super)conformal field theory
A long-standing problem is the disagreement between supergravity and conformal field theory on the free energy of the system. The latter gives a result which is 3/4 of the former. These calculations are particularly interesting, as the AdS/CFT correspondence probes the strong-coupling regime of super Yang-Mills theory for large N. This indicates that an understanding of the number of degrees of freedom contributing to the free energy is lacking. Dr. Siopsis and his collaborator, Dr. A. Petkou, started investigating this problem from the conformal field theory point of view. They started with a finite temperature conformal field theory in three dimensions. In that case one obtains a non-trivial fixed point whose free energy is 4/5 the free energy of the trivial point. They constructed a model that interpolated between the two critical points and showed in detail how certain degrees of freedom decoupled along the flow. They thus showed explicitly that one critical point had 4/5 the number of degrees of freedom of the other. The result required non-trivial polylogarithm identities [31]. It would be interesting to extend these results to two dimensions (finding invariants along the flow connecting critical models with each other at finite temperature) and four dimensions (where the D-brane system may correspond to a non-trivial critical point on the CFT side). |
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