On semiclassical approximation and spinning string vertex operators in AdS_5 x S^5

TL;DR

This paper investigates the structure and renormalization of vertex operators representing semiclassical string states with large energy and angular momentum in AdS_5 x S^5, providing insights into their anomalous dimensions and semiclassical relations.

Contribution

It clarifies the structure of semiclassical vertex operators, analyzes their 1-loop anomalous dimensions, and explores the derivation of semiclassical relations from vertex operator marginality.

Findings

Identified operators with tunable small anomalous dimensions at 1-loop.

Analyzed the leading-order renormalization of vertex operators in AdS_5 x S^5.

Discussed a method to derive nd S/rom marginality conditions.

Abstract

Following earlier work by Polyakov and Gubser, Klebanov and Polyakov, we attempt to clarify the structure of vertex operators representing string states which have large (``semiclassical'') values of AdS energy (equal to 4-d dimension \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' perturbative expansion for the 2-d anomalous dimensions of the corresponding vertex operators. We consider in detail the leading-order 1-loop renormalization of these operators in AdS_5 x S^5 sigma model (ignoring fermionic contributions). We find new examples of operators for which, as in the case considered in hep-th/0110196, 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 \Delta 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.