Bulk quartic vertices from boundary four-point correlators

TL;DR

This paper explores the notion of locality in bulk higher-spin gravity duals of weakly-coupled conformal field theories, focusing on Mellin amplitudes in the context of $O(N)$ vector models and higher-spin gravity.

Contribution

It provides arguments suggesting refined locality properties in higher-spin holography and analyzes boundary correlators using Mellin amplitudes for scalar operators.

Findings

Higher-spin gravity duals exhibit a refined form of locality.

Mellin amplitude analysis supports the locality conjecture.

Results are based on three- and four-point scalar correlators.

Abstract

We present arguments which suggest that the bulk higher-spin gravity duals of weakly-coupled conformal field theories obey some refined notion of locality. In particular, we discuss the Mellin amplitude programme in this context. We focus on the $O(N)$ vector model and minimal higher-spin gravity as a paradigmatic example of such holographic dual pairs. We restrict ourselves to three- and four-point functions of scalar primary operators, but the qualitative conclusions are expected to hold for the generic case.