Three point functions in higher spin AdS_3 supergravity

TL;DR

This paper provides further evidence for the duality between higher spin supergravity on AdS_3 and a specific conformal field theory by computing and comparing three-point correlation functions involving fermionic and bosonic operators.

Contribution

It calculates boundary three-point functions in higher spin AdS_3 supergravity and confirms their agreement with dual CFT results, leveraging supersymmetry for validation.

Findings

Boundary three-point functions match between supergravity and CFT.

Supersymmetry simplifies correlator computations and confirms conjectures.

Results support the proposed AdS/CFT duality for higher spin supergravity.

Abstract

In a previous work we have proposed that the Prokushkin-Vasiliev higher spin N=2 supergravity on AdS_3 is dual to a large N limit of the N=(2,2) CP^N Kazama-Suzuki model. There is now strong evidence supporting this proposal based on symmetry and spectrum comparison. In this paper we will give further evidence for the duality by studying correlation functions. We compute boundary three point functions with two fermionic operators and one higher spin bosonic current in terms of the bulk supergravity theory. Then we compare with the results in the dual CFT, where the supersymmetry of the theory turns out to be very helpful. In particular we use it to confirm results conjectured in the bosonic case. Moreover, correlators with a fermionic current can be obtained via supersymmetry.