Holographic Representation of Higher Spin Gauge Fields

TL;DR

This paper constructs holographic bulk operators for higher spin gauge fields in AdS space, demonstrating their representation via boundary integrals, analyzing their two-point functions, and extending the approach to de Sitter spacetime.

Contribution

It introduces a method to represent higher spin gauge fields holographically in AdS, extending previous work to include integer spins greater than one and analyzing their correlation functions.

Findings

Higher spin gauge fields are represented by boundary integrals over a bulk lightcone region.

Two-point functions show singularities on both bulk and boundary lightcones.

The construction is extended to de Sitter spacetime with a causal approach.

Abstract

Extending the results of \cite{Heem}, \cite{KLRS} on the holographic representation of local gauge field operators in anti de Sitter space, here we construct the bulk operators for higher spin gauge fields in the leading order of $\frac{1}{N}$ expansion. Working in holographic gauge for higher spin gauge fields, we show that gauge field operators with integer spin $s>1$ can be represented by an integration over a ball region, which is the interior region of the spacelike bulk lightcone on the boundary. The construction is shown to be AdS-covariant up to gauge transformations, and the two-point function between higher spin gauge fields and boundary higher spin current exhibit singularities on both bulk and boundary lightcones. We also comment on possible extension to the level of three-point functions and carry out a causal construction for higher spin fields in de Sitter spacetime.