Comments on the Mirror TBA

TL;DR

This paper analyzes the structure of excited state TBA equations in AdS/CFT, revealing that auxiliary roots are not essential for their derivation and that these equations encode entire superconformal multiplets, reflecting underlying symmetry.

Contribution

It clarifies the role of auxiliary roots in TBA equations and shows these equations describe superconformal multiplets rather than individual states.

Findings

Auxiliary roots do not influence excited state TBA equations.

TBA equations encode entire superconformal multiplets.

PSU(2,2|4) invariance is inherent in the TBA construction.

Abstract

We discuss various aspects of excited state TBA equations describing the energy spectrum of the AdS_5 \times S^5 strings and, via the AdS/CFT correspondence, the spectrum of scaling dimensions of N = 4 SYM local operators. We observe that auxiliary roots which are used to partially enumerate solutions of the Bethe-Yang equations do not play any role in engineering excited state TBA equations via the contour deformation trick. We further argue that the TBA equations are in fact written not for a particular string state but for the whole superconformal multiplet, and, therefore, the psu(2,2|4) invariance is built in into the TBA construction.