Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution

TL;DR

This paper introduces a new gauge for the linearized Didenko-Vasiliev solution in higher-spin gravity, proving its holographic duality with boundary correlators and providing explicit bulk-boundary correspondence results.

Contribution

It presents a novel gauge for the Didenko-Vasiliev solution and proves the holographic duality between bulk interactions and boundary correlators in higher-spin gravity.

Findings

New gauge for the Didenko-Vasiliev solution in AdS_4

Proof of holographic duality between bulk action and boundary correlators

Reproduction of boundary-bulk propagators for all spins

Abstract

We consider type-A higher-spin gravity in AdS_4, holographically dual to a free U(N) vector model on the boundary. We study the linearized version of the Didenko-Vasiliev "BPS black hole", which we view as this theory's equivalent of the fundamental string. The Didenko-Vasiliev solution consists of gauge fields of all spins generated by a particle-like source along a bulk geodesic, and is holographically dual to a bilocal boundary operator at the geodesic's endpoints. Our first main result is a new gauge for this solution, which makes manifest its behavior under the boundary field equation. It can be viewed as an AdS uplift of flat spacetime's de Donder gauge, but is not de Donder in AdS. To our knowledge, this gauge is novel even in the spin-2 sector, and thus provides a new expression for the linearized gravitational field of a massive point particle in (A)dS_4. Our second main result is a proof of the holographic duality between the mutual bulk action of two Didenko-Vasiliev solutions and the CFT correlator of two boundary bilocals. As an intermediate step, we show that in a bilocal->local limit, the Didenko-Vasiliev solution reproduces the standard boundary-bulk propagators of all spins. We work in the "metric-like" language of Fronsdal fields, and use the embedding-space formalism.