First-principles derivation of the AdS/CFT Y-systems

TL;DR

This paper derives the AdS5/CFT4 Y-system from first principles using quantum effects in transfer matrix fusion, providing a rigorous foundation for solving the spectrum problem in N=4 SYM.

Contribution

It offers a perturbative, first-principles derivation of the AdS/CFT Y-system based on quantum corrections in transfer matrices, extending previous heuristic approaches.

Findings

Quantum corrections induce correct spectral parameter shifts.

UV divergences in line operators analyzed up to first order.

Fusion of line operators computed up to second order.

Abstract

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.