From Spacetime to Worldsheet: Four point correlators

TL;DR

This paper derives explicit four-point correlators on the string worldsheet from large N field theory using Schwinger parameters, revealing properties consistent with a 2D CFT and applicable to AdS/CFT correspondence.

Contribution

It provides a systematic method to compute full worldsheet four-point functions from Schwinger parameters, advancing the understanding of string duals of large N field theories.

Findings

Derived explicit four-point correlator expressions obeying crossing symmetry.

Established a connection between Schwinger parameters and worldsheet cross ratios.

Developed a framework for systematic perturbation expansion of correlators.

Abstract

The Schwinger representation gives a systematic procedure for recasting large N field theory amplitudes as integrals over closed string moduli space. This procedure has recently been applied to a class of free field four point functions by Aharony, Komargodski and Razamat, to study the leading terms in the putative worldsheet OPE. Here we observe that the dictionary between Schwinger parameters and the cross ratio of the four punctured sphere actually yields an explicit expression for the full worldsheet four point correlator in many such cases. This expression has a suggestive form and obeys various properties, such as crossing symmetry and mutual locality, expected of a correlator in a two dimensional CFT. Therefore one may take this to be a candidate four point function in a worldsheet description of closed strings on highly curved AdS_5 \times S^5. The general framework, that we develop for computing the relevant Strebel differentials, also admits a systematic perturbation expansion which would be useful for studying more general four point correlators.