Higher Spin Gauge Theory and Holography: The Three-Point Functions

TL;DR

This paper computes three-point functions in Vasiliev's higher spin gauge theory in AdS4 and confirms their agreement with free and critical O(N) vector models, supporting the holographic duality conjecture.

Contribution

It provides the first explicit calculation of three-point functions in Vasiliev's theory, confirming its duality with free and critical O(N) models.

Findings

Agreement with free scalar field correlators in three dimensions.

Agreement with critical O(N) vector model correlators under alternative boundary conditions.

Supports the conjecture that Vasiliev theory is holographically dual to free and critical O(N) models.

Abstract

In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.