Semiclassical correlators of three states with large S^5 charges in string theory in AdS_5 x S^5

TL;DR

This paper develops a semiclassical method to compute 3-point correlation functions of string states with large charges in AdS_5 x S^5, using geodesic configurations and Schwarz-Christoffel maps, and verifies results against supergravity and gauge theory.

Contribution

It introduces a novel semiclassical approach combining geodesic configurations and conformal maps for 3-point correlators in AdS/CFT, extending previous methods to non-BPS states and specific string configurations.

Findings

Derived explicit semiclassical expressions for 3-point correlators.

Confirmed agreement with supergravity and gauge theory in BPS cases.

Applied method to various extremal and non-extremal correlators.

Abstract

We consider semiclassical computation of 3-point correlation functions of (BPS or non-BPS) string states represented by vertex operators carrying large charges in S5. We argue that the AdS5 part of the construction of relevant semiclassical solution involves the two basic ingredients: (i) configuration of three glued geodesics in AdS2 suggested by Klose and McLoughlin in arXiv:1106.0495 and (ii) a particular Schwarz-Christoffel map of the 3-geodesic solution in cylindrical (tau, sigma) domain into the complex plane with three marked points. This map is constructed using the expression for the AdS2 string stress tensor which is uniquely determined by the 3 scaling dimensions as noted by Janik and Wereszczynski in arXiv:1109.6262 (our solution, however, is different from theirs). We also find the S5 part of the solution and thus the full expression for the semiclassical part of the 3-point correlator for several examples: extremal and non-extremal correlators of BPS states and a particular correlator of "small" circular spinning strings in S3 part of S5. We demonstrate that for the BPS correlators the results agree with the large charge limit of the corresponding supergravity and free gauge theory expressions.