New diagrammatic framework for higher-spin gravity

TL;DR

This paper introduces a new diagrammatic framework for minimal higher-spin gravity in four dimensions, enabling the calculation of n-point functions and connecting field theory and string theory approaches.

Contribution

It proposes novel diagrammatic rules involving Fronsdal fields and Didenko-Vasiliev particles, providing a bulk realization of higher-spin algebra and reproducing holographic correlators.

Findings

New diagrammatic rules for higher-spin gravity are established.

The framework reproduces all n-point functions of the dual free O(N) vector model.

The rules interpolate between field theory and string theory diagrams.

Abstract

We consider minimal type-A higher-spin (HS) gravity in four dimensions, at tree level. We propose new diagrammatic rules for this theory, involving both Fronsdal fields and Didenko-Vasiliev (DV) particles - linearized versions of HS gravity's "BPS black hole". The vertices include a standard minimal coupling between particle and gauge field, the Sleight-Taronna cubic vertex for HS fields, and a recently introduced vertex coupling two HS fields to a DV particle. We show how these ingredients can be combined to reproduce all n-point functions of the theory's holographic dual - the free O(N) vector model. Our diagrammatic rules interpolate between the usual ones of field theory and those of string theory. Our construction can be viewed as a bulk realization of HS algebra.