Quasi-local formulation of the mirror TBA

TL;DR

This paper introduces a quasi-local reformulation of the mirror TBA equations for the AdS/CFT spectral problem, eliminating infinite sums and simplifying the analysis of Y-functions.

Contribution

It presents a novel quasi-local formulation of the mirror TBA system that reduces complexity by removing infinite sums and connecting Y-functions locally.

Findings

Infinite sums are eliminated from TBA equations.

Y-functions are connected at most to next-to-nearest neighbors.

Simplifies the analysis of the AdS/CFT spectral problem.

Abstract

We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are connected by the TBA equations are at most next to nearest neighbors with respect to the Y-system diagram of AdS/CFT.