Hybrid-NLIE for the AdS/CFT spectral problem

TL;DR

This paper introduces a new finite Nonlinear Integral Equation (NLIE) approach for solving the spectral problem in AdS/CFT, simplifying the TBA equations by replacing certain parts with a few complex variables, and confirms its accuracy through analytical corrections.

Contribution

It develops a hybrid NLIE method that replaces parts of the TBA equations with a finite set of variables, providing an explicit and simplified formulation for the AdS/CFT spectral problem.

Findings

Derived explicit NLIE equations for the ground state of gamma-deformed AdS/CFT.

Calculated the first correction to the asymptotic solution analytically.

Found agreement with original TBA results, differing from recent FiNLIE formulations.

Abstract

Hybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its gamma-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a few appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. The integral equations are written explicitly for the ground state of the gamma-deformed system. We linearize these NLIE equations, analytically calculate the first correction to the asymptotic solution and find agreement with analogous results coming from the original TBA formalism. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.