Exploring the mirror TBA

TL;DR

This paper applies the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 imes S^5 mirror model, revealing state-dependent equations and the existence of infinitely many critical coupling values affecting excited state energies.

Contribution

It introduces a state-specific formulation of TBA equations for the mirror model and uncovers the critical coupling phenomena impacting excited state calculations.

Findings

Each state has its own set of TBA equations.

Infinitely many critical 't Hooft coupling values exist.

Estimated first critical value is approximately 774 for the Konishi operator.

Abstract

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.