Solving the AdS/CFT Y-system

TL;DR

This paper simplifies the complex AdS/CFT Y-system into a finite set of nonlinear integral equations using integrability and symmetry properties, enabling more efficient analysis of the system.

Contribution

It introduces a novel finite set of nonlinear integral equations for the AdS/CFT Y-system leveraging Z4 symmetry and Wronskian parameterization, improving analytical tractability.

Findings

Reproduces numerical results for the Konishi operator

Provides a deeper understanding of the Y- and T-functions' analyticity

Simplifies the original infinite Y-system into a finite form

Abstract

Using integrability and analyticity properties of the AdS5/CFT4 Y-system we reduce it to a finite set of nonlinear integral equations. The Z4 symmetry of the underlying coset sigma model, in its quantum version, allows for a deeper insight into the analyticity structure of the underlying Y-functions and T-functions, as well as for their analyticity friendly parameterization in terms of Wronskian determinants of Q-functions. As a check for the new equations, we reproduce the numerical results for the Konishi operator previously obtained from the original infinite Y-system.