Semiclassical quantization of superstrings: AdS₅ x S⁵ and beyond

We discuss semiclassical quantization of closed superstrings in AdS_5 x S^5. We consider two basic examples: point-like string boosted along large circle of S^5 and folded string rotating in AdS_5. In the first case we clarify the general structure of the sigma model perturbation theory for the energy of string states beyond the leading 1-loop order (related to the plane-wave limit). In the second case we argue that the large spin limit of the expression for the ground-state energy (i.e. for the dimension of the corresponding minimal twist gauge theory operator) has the form S + f(\lambda) \ln S to all orders in \alpha' ~ \lambda^{-1/2} expansion, in agreement with the AdS/CFT duality. We also suggest an extension of the semiclassical approach to near-conformal (near-AdS) cases on the example of the fractional D3-brane on conifold background. Expanded version of talks at the Third International Sakharov Conference on Physics, Moscow, June 24-29, 2002 and at Strings 2002, Cambridge, July 15-20,2002