Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory

TL;DR

This paper explores the locality of quartic interactions in higher-spin gravity within AdS/CFT correspondence, deriving explicit bulk scalar vertices from boundary conformal correlators, revealing a generalized notion of locality.

Contribution

It provides the first explicit form of the quartic scalar vertex in higher-spin gravity from conformal field theory data, demonstrating a generalized locality property.

Findings

Explicit quartic scalar vertex derived from boundary four-point functions.

Established conformal block expansions for boundary and bulk amplitudes.

The vertex satisfies a generalized locality condition.

Abstract

Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS$_4$ and the free $O\left(N\right)$ vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.