Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity

TL;DR

This paper explores how bulk cubic correlators in higher-spin gravity, dual to a free vector model, can be extended from local to bilocal boundary operators, revealing gauge invariance and new bulk structures involving Didenko-Vasiliev solutions.

Contribution

It extends the understanding of bulk-boundary correspondence in higher-spin gravity by incorporating bilocal operators and demonstrating gauge invariance of the cubic vertex beyond previous limitations.

Findings

Bulk cubic correlators can be represented by local structures including a new vertex.

The Sleight-Taronna vertex is gauge-invariant in general traceless gauge.

Numerical analysis confirms the correlator involving local and bilocal operators.

Abstract

We consider type-A higher-spin gravity in 4 dimensions, holographically dual to a free O(N) vector model. In this theory, the cubic correlators of higher-spin boundary currents are reproduced in the bulk by the Sleight-Taronna cubic vertex. We extend these cubic correlators from local boundary currents to bilocal boundary operators, which contain the tower of local currents in their Taylor expansion. In the bulk, these boundary bilocals are represented by linearized Didenko-Vasiliev (DV) "black holes". We argue that the cubic correlators are still described by local bulk structures, which include a new vertex coupling two higher-spin fields to the "worldline" of a DV solution. As an illustration of the general argument, we analyze numerically the correlator of two local scalars and one bilocal. We also prove a gauge-invariance property of the Sleight-Taronna vertex outside its original range of applicability: in the absence of sources, it is invariant not just within tranverse-traceless gauge, but rather in general traceless gauge, which in particular includes the DV solution away from its "worldline".