Y-system and beta-deformed N=4 Super-Yang-Mills

TL;DR

This paper demonstrates how the Y-system approach can reproduce perturbation theory results for operator anomalous dimensions in beta-deformed N=4 Super-Yang-Mills, revealing new insights into the integrals involved.

Contribution

It introduces a twisted asymptotic solution of the Y-system that captures the effects of the deformation parameter beta, linking integrability with perturbation theory results.

Findings

Reproduces known perturbation theory results from the Y-system.

Derives a generating function for a class of perturbative integrals.

Shows the role of the beta parameter in extracting perturbative information.

Abstract

We show how the perturbation theory results recently obtained by F.Fiamberti, A.Santambrogio, C.Sieg and D.Zanon for operator anomalous dimensions of beta-deformed Super-Yang-Mills theory can be reproduced from the AdS5/CFT4 Y-system proposed by N.G., V.Kazakov and P.Vieira. To do this, we obtain the general twisted asymptotic solution of this Y-system of functional equations. We show that existence of an additional parameter beta in the deformed theory allows to extract rich information about the perturbation theory integrals directly from Y-system. Using this method we found a simple generating function for a broad class of such integrals.