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.Comment: 28 pages, 1 figure, v2: misprints are correcte