New diagrammatic framework for higher-spin gravity

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.

5 pages + 15 pages of appendices, 1 figure + 31 diagrams; v2: PRL version - expanded exposition and examples, corrected some combinatorics

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