Bulk quartic vertices from boundary four-point correlators

TL;DR

The paper investigates how bulk locality can be refined in higher-spin holography, using Mellin amplitudes to diagnose locality/nonlocality in AdS duals of weakly-coupled CFTs, with a focus on the $O(N)$ vector model and its minimal higher-spin gravity dual. It argues that quartic bulk interactions can exhibit weak locality, characterized by 4-point contact Witten diagrams that are entire in Mellin variables, provided exchange diagrams account for single-trace data. A concrete holographic reconstruction in $AdS_4$ of the quartic scalar vertex is presented, showing a sum over even spins with entire generating functions, which supports the weak-locality picture, though it also highlights subtle infinities and on-shell independence issues. The analysis of Mellin amplitudes for the free and critical $O(N)$ models reveals distributional, non-analytic behavior that may preclude a standard flat-space limit, underscoring the special nature of higher-spin duals and guiding future refinements of locality criteria in holography.

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.

Figures (2)

• Figure 1: Four-point Witten diagrams contributing to the holographic reconstruction.
• Figure 2: Comparison of exchange and contact Witten diagrams in a single channel.