MS Seminar (Mathematics - String Theory)

Speaker: Zengo Tsuboi (Osaka City University)
Title: Wronskian solutions of T, Q and Y-systems for AdS/CFT
Date: Tue, Sep 07, 2010, 13:15 - 14:45
Place: Seminar Room A
Abstract: In 2009, Gromov, Kazakov and Vieira proposed a set of functional relations called the Y-system for the exact spectrum of AdS/CFT. This Y-system is equivalent to a T-system (Hirota equations) defined on the T-hook boundary condition. In the strong coupling limit, the shift of the spectral parameter of the T-system can be neglected, and it reduces to a simplified system of equations called the Q-system. We construct a solution of this Q-system. This solution appears to be a set of supercharcters of SU(2,2|4) group in unitary representations with the classical AdS_5 x S5 superstring monodromy matrix as the group element. Generalizing this solution of the Q-system, we construct Wronskian-like finite size determinant solutions of the T-system for AdS/CFT. We also found Wronskian-like determinant solutions of the T-systems for more general T-hook boundary conditions related to infinite dimensional representations of gl(M|N).
(Refs: arXiv:1002.3981[hep-th]; arXiv:0906.2039 [math-ph])

Part 1: I will talk about T, Q and Y-systems in general.

Part 2: I will talk about Wronskian solutions of the T-system for super spin chains, which I proposed in 1997. This T-system is defined on the [M,N]-hook of gl(M|N), and is closely related to the T-system for AdS/CFT. In fact, the T-hook for AdS/CFT is a union of two copies of the [2,2]-hook for gl(2|2). Next, I will talk about solutions of the Q-system for AdS/CFT. Finally, I will explain our Wronskian solutions of the T-system for AdS/CFT.