On semiclassical approximation and spinning string vertex operators in AdS5 x S5

Following earlier work by Polyakov and Gubser, Klebanov and Polyakov, we attempt to clarify the structure of vertex operators representing particular string states which have large (semiclassical) values of AdS energy or 4d dimension E = Delta and angular momentum J in S-5 or spin S in AdS(5). We comment on the meaning of semiclassical limit in the context of alpha' similar to 1/rootalpha perturbative expansion for the 2d anomalous dimensions of the corresponding vertex operators. We consider in detail the leading-order 1-loop renormalization of these operators in AdS5 X S5 sigma model (ignoring fermionic contributions). We find more examples of operators (in addition to the one in hep-th/0110196) for which the 1-loop anomalous dimension can be made small by tuning quantum numbers. We also comment on a possibility of deriving the semiclassical relation between A and J or S from the marginality condition for the vertex operators, using a stationary phase approximation in the path integral expression for their 2-point correlator on a complex plane. (C) 2003 Elsevier B.V. All rights reserved.