Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)

TL;DR

This paper extends Wronskian solutions of the T-system for the general linear superalgebra gl(M|N), connecting them to supercharacter formulas of infinite-dimensional modules and applications in AdS/CFT spectral problems.

Contribution

It generalizes Wronskian solutions from [M,N]-hooks to the full T-hook for gl(M|N), linking to supercharacter formulas and integrable models.

Findings

Derived Wronskian solutions for the general T-hook

Connected solutions to supercharacter formulas of unitarizable modules

Included applications to AdS5/CFT4 spectral problem

Abstract

In [Z.Tsuboi, Nucl. Phys. B 826 (2010) 399 [arXiv:0906.2039]], we proposed Wronskian-like solutions of the T-system for [M,N]-hook of the general linear superalgebra gl(M|N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1,N1]-hook and [M2,N2]-hook (M=M1+M1, N=N1+N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl(M|N). Our solutions also include a Wronskian-like solution discussed in [N.Gromov, V.Kazakov, S.Leurent, Z.Tsuboi, JHEP 1101 (2011) 155 [arXiv:1010.2720]] in relation to the AdS5/CFT4 spectral problem.