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Following our earlier work in arXiv:0906.4294 we show how to usesemiclassical string quantization approach to compute the leading correctionsto the energy of AdS_5 x S^5 string states on the first excited string levelthat should correspond to operators in the Konishi multiplet of N=4 SYM theory.Compared to examples in our previous paper the string solutions we considerhere carry an extra component of S^5 angular momentum J. This facilitates theiridentification with operators in the Konishi multiplet. We show that for suchstring states with J=2 the coefficient of the subleading lambda^(-1/4) term inthe large string tension expansion of the energy is twice the one found inarXiv:0906.4294. The resulting value matches the one found for the Konishistate in the sl(2) sector from the Y-system/TBA approach, resolving an apparentdisagreement claimed earlier.

Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet