On holographic three point functions for GKP strings from integrability

TL;DR

This paper develops an integrability-based method to compute holographic three-point functions for large spin GKP strings, introducing new techniques like a generalized Riemann bilinear identity to handle singularities.

Contribution

It extends integrability methods from gluon scattering to holographic three-point functions of GKP strings, incorporating new mathematical tools for singularity management.

Findings

Derived a generalized Riemann bilinear identity for singular cases

Established a systematic approach for constructing semiclassical vertex operators

Expressed area integrals as contour integrals in the presence of singularities

Abstract

Adapting the powerful integrability-based formalism invented previously for the calculation of gluon scattering amplitudes at strong coupling, we develop a method for computing the holographic three point functions for the large spin limit of Gubser-Klebanov- Polyakov (GKP) strings. Although many of the ideas from the gluon scattering problem can be transplanted with minor modifications, the fact that the information of the external states is now encoded in the singularities at the vertex insertion points necessitates several new techniques. Notably, we develop a new generalized Riemann bilinear identity, which allows one to express the area integral in terms of appropriate contour integrals in the presence of such singularities. We also give some general discussions on how semiclassical vertex operators for heavy string states should be constructed systematically from the solutions of the Hamilton-Jacobi equation.