Matching four-point functions in higher spin AdS_3/CFT_2

TL;DR

This paper computes and matches four-point functions in 3D higher spin gravity and 2D W_N minimal models, demonstrating precise agreement and establishing new computational rules for correlation functions in higher spin theories.

Contribution

It provides the first functional form computation of a 3D higher spin gravity correlator not fixed by conformal symmetry, using matrix methods and Coulomb gas techniques.

Findings

Exact agreement between bulk and boundary four-point functions.

Development of rules for multi-trace operator correlators in higher spin gravity.

Method applicable to both sl(N) and hs[inity] theories.

Abstract

Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is the first computation of a correlator in 3D higher spin gravity whose functional form is not fixed by conformal invariance. In the bulk we make use of elegant methods to solve the scalar field equation using only matrix manipulations, while on the CFT side we employ the Coulomb gas representation. Comparison is made in the semiclassical limit, in which the central charge is taken to infinity at fixed N. Along the way, we establish the rules for computing correlation functions of multi-trace operators in higher spin gravity. The method involves solving the scalar master field equation in a general representation of the bulk gauge algebra. Although most of our work is carried out for the bulk theory based on sl(N) x sl(N), we also discuss how our methods can be adapted to the hs[\lambda] x hs[\lambda] theory, which is relevant in the 't Hooft limit.