The Hirota equation for string theory in AdS5xS5 from the fusion of line operators

TL;DR

This paper derives the T-system for planar N=4 SYM and related string theories using a perturbative approach based on the fusion of line operators, providing a first-order semi-classical proof without assumptions.

Contribution

It offers a novel perturbative derivation of the T-system from line operator fusion, applicable to string theories in AdS spaces, extending previous non-perturbative insights.

Findings

T-system holds at first order in semi-classical expansion

Derivation does not rely on assumptions

Applicable to various AdS string models

Abstract

We present a perturbative derivation of the T-system that is believed to encode the exact spectrum of planar N=4 SYM. The T-system is understood as an operator identity between some special line operators, the quantum transfer matrices. By computing the quantum corrections in the process of fusion of transfer matrices, we show that the T-system holds up to first order in a semi-classical expansion. This derivation does not rely on any assumption. We also discuss the extension of the proof to other theories, including models describing string theory on various AdS spaces.