On correlation functions of operators dual to classical spinning string states

TL;DR

This paper develops a method to compute correlation functions of operators dual to classical spinning strings at strong coupling, revealing a complex structure of 'fattened' Witten diagrams and their subtle evaluation.

Contribution

It introduces a modified classical action approach for calculating correlation functions involving spinning string states, including the derivation of two- and three-point functions.

Findings

Reproduces correct scaling with anomalous dimensions

Identifies the need for a wave function projection in calculations

Provides a framework for three-point function spacetime dependence

Abstract

We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out to be surprisingly subtle and requires a modification of the naive classical action due to a necessary projection onto appropriate wave functions. We examine string solutions which compute the simplest case of a two-point function and reproduce the right scaling with the anomalous dimensions corresponding to the energies of the associated spinning string solutions. We also describe, under some simplifying assumptions, how the spacetime dependence of a conformal three-point correlation function arises in this setup.