Bulk interactions and boundary dual of higher-spin-charged particles

TL;DR

This paper explores higher-spin gravity in AdS_4, revealing how interactions between charged particles cancel divergences and correspond to boundary bilocal operators, providing insights into bulk-boundary duality and non-locality.

Contribution

It demonstrates the cancellation of UV divergences in higher-spin interactions and identifies bulk particles as duals of boundary bilocal operators using twistor methods.

Findings

UV divergences cancel when particles are close, for almost any velocity

Bulk particles correspond to boundary bilocal operators via twistor transform

Interaction is represented by geodesic Witten diagrams calculating boundary correlators

Abstract

We consider higher-spin gravity in (Euclidean) AdS_4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity's famous feature, the cancellation of the electric and gravitational forces between two BPS particles at rest. In the holographic context, we point out that these "Didenko-Vasiliev particles" are just the bulk duals of bilocal operators in the boundary theory. For this identification, we use the Penrose transform between bulk fields and twistor functions, together with its holographic dual that relates twistor functions to boundary sources. In the resulting picture, the interaction between two Didenko-Vasiliev particles is just a geodesic Witten diagram that calculates the correlator of two boundary bilocals. We speculate on implications for a possible reformulation of the bulk theory, and for its non-locality issues.