Wave functions and correlation functions for GKP strings from integrability

TL;DR

This paper introduces a general method for computing vertex operator contributions to semi-classical correlation functions of heavy strings, specifically applied to three-point functions of GKP strings in AdS3, advancing understanding of string interactions.

Contribution

The authors develop a new method based on local saddle point behavior that applies even without explicit vertex operator forms, and they compute three-point functions for GKP strings in AdS3.

Findings

Successfully computed three-point functions with correct boundary coordinate dependence

Method applicable to cases with unknown vertex operator forms

Finite three-point functions consistent with theoretical expectations

Abstract

We develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in $AdS_3$ spacetime, left unevaluated in our previous work [arXiv:1110.3949] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.