Comments on the Mirror TBA

Understand

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.