Quantum strings in AdS5 x S5: strong-coupling corrections to dimension of Konishi operator

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS(5) x S-5, which should be dual to members of the Konishi operator multiplet in N - 4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta = 2 lambda(1/4) vertical bar b(0) vertical bar b(1)lambda(-1/4) vertical bar b(3)lambda(-3/4) vertical bar ..., 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 canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b(1) - 1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.