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

Following our earlier work in arXiv:0906.4294 we show how to use semiclassical string quantization approach to compute the leading corrections to the energy of AdS5×S5 string states on the first excited string level that should correspond to operators in the Konishi multiplet of N=4 SYM theory. Compared to examples in our previous paper the string solutions we consider here carry an extra component of S5 angular momentum J. This facilitates their identification with operators in the Konishi multiplet. We show that for such string states with J=2 the coefficient of the subleading λ−1/4 term in the large string tension expansion of the energy is twice the one found in arXiv:0906.4294. The resulting value matches the one found for the Konishi state in the sl(2) sector from the Y-system/TBA approach, resolving an apparent disagreement claimed earlier.