PSU(2,2|4) Character of Quasiclassical AdS/CFT

TL;DR

This paper solves the T- and Y-systems for the exact spectrum of AdS/CFT in the strong coupling limit, revealing super-characters of SU(2,2|4) and matching quasiclassical string quantization results.

Contribution

It provides a novel solution to the T- and Y-systems for AdS/CFT spectrum and introduces a Weyl-type formula for T-functions as super-characters.

Findings

T-functions are super-characters of SU(2,2|4)

The formula reproduces quasiclassical one-loop results

Proposes a link between T-functions and quantum monodromy

Abstract

We solve the recently proposed T- and Y-systems (Hirota equation) for the exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary quasiclassical string state. The corresponding T-functions appear to be super-characters of the SU(2,2|4) group in unitary representations with a highest weight, with the classical AdS5xS5 superstring monodromy matrix as the group element. We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions. We also speculate about possible relation between the T-functions and the quantum monodromy matrix.