Planar solutions of higher-spin theory I: free field level

TL;DR

This paper constructs free field solutions for higher-spin gauge fields in an AdS black brane background, extending known gravitational solutions to include higher spins with symmetry properties suitable for future nonlinear studies.

Contribution

It presents the first explicit free field higher-spin generalization of an AdS black brane that respects static and planar symmetry for all bosonic spins.

Findings

Derived solutions for higher-spin curvatures and potentials.

Solutions satisfy multi copy relation.

Framework suitable for nonlinear analysis.

Abstract

Many black hole solutions of General Relativity are known to be linearly exact. This opens a way to study them in gauge theories that apart from gravity contain fields of higher spin $s>2$. Starting with a black brane in $AdS_4$ we find its free field higher-spin generalization that respects static and planar symmetry for all bosonic gauge fields $s\geq 0$. The solution is found for both the higher-spin curvatures and potentials in the form suitable for further non-linear analysis and satisfies the multi copy relation.