Scalar fields and three-point functions in D=3 higher spin gravity

TL;DR

This paper calculates three-point functions involving scalars and higher spin gauge fields in AdS3, providing evidence for the duality between Vasiliev's higher spin gravity and W_{inity}[ extlambda] CFTs, and develops new tools for analyzing higher spin backgrounds.

Contribution

It introduces methods to extract scalar field equations in higher spin backgrounds and computes boundary correlators matching CFT predictions, supporting the AdS/CFT duality in higher spin theories.

Findings

Boundary three-point functions match CFT expectations.

Results support the duality between higher spin gravity and W_{inity}[ extlambda] CFTs.

Developed tools for analyzing scalar fields in higher spin backgrounds.

Abstract

We compute boundary three-point functions involving two scalars and a gauge field of arbitrary spin in the AdS vacuum of Vasiliev's higher spin gravity, for any deformation parameter \lambda. In the process, we develop tools for extracting scalar field equations in arbitrary higher spin backgrounds. We work in the context of hs[\lambda] + hs[\lambda] Chern-Simons theory coupled to scalar fields, and make efficient use of the associative lone-star product underlying the hs[\lambda] algebra. Our results for the correlators precisely match expectations from CFT; in particular they match those of any CFT with W_{\infinity}[\lambda] symmetry at large central charge, and with primary operators dual to the scalar fields. As this is expected to include the `t Hooft limit of the W_N minimal model CFT, our results serve as further evidence of the conjectured AdS/CFT duality between these two theories.