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We consider leading strong coupling corrections to the energy of the lightestmassive string modes in AdS_5 x S^5, which should be dual to members of theKonishi operator multiplet in N=4 SYM theory. This determines the generalstructure of the strong-coupling expansion of the anomalous dimension of theKonishi operator. We use 1-loop results for several semiclassical string statesto extract information about the leading coefficients in this expansion. Ourprediction is  Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +...,where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3).Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonicaldimension of the corresponding gauge-theory operator in the Konishi multiplet)and b_1=1. Our conclusions are sensitive to few assumptions, implied by acorrespondence with flat-space expressions, on how to translate semiclassicalquantization results into predictions for the exact quantum string spectrum.

Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator