On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT

TL;DR

This paper computes the semiclassical two-point function of large spin string states in AdS_5, showing it matches the strong-coupling gauge theory predictions and relating the solution to classical folded spinning strings.

Contribution

It provides a semiclassical approximation method for correlators of string vertex operators with large spin in AdS/CFT, connecting the solutions to classical string configurations.

Findings

The two-point function matches the expected form from gauge theory.

The semiclassical solution relates to the large spin limit of folded spinning strings.

Source terms encode quantum numbers of the string states.

Abstract

We consider the 2-point function of string vertex operators representing string state with large spin in AdS_5. We compute this correlator in the semiclassical approximation and show that it has the expected (on the basis of state-operator correspondence) form of the strong-coupling limit of the 2-point function of single trace minimal twist operators in gauge theory. The semiclassical solution representing the stationary point of the path integral with two vertex operator insertions is found to be related to the large spin limit of the folded spinning string solution by a euclidean continuation, transformation to Poincare coordinates and conformal map from cylinder to complex plane. The role of the source terms coming from the vertex operator insertions is to specify the parameters of the solution in terms of quantum numbers (dimension and spin) of the corresponding string state. Understanding further how similar semiclassical methods may work for 3-point functions may shed light on strong-coupling limit of the corresponding correlators in gauge theory as was recently suggested by Janik et al in arXiv:1002.4613.