Holographic representation of higher spin gauge fields

Abstract

Extending the results of [1,2] 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 at the leading order in $\frac{1}{N}$ expansion. Working in the 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 light cone on the boundary. The construction is shown to be anti--de Sitter covariant up to gauge transformations, and the two-point function between higher spin gauge fields and the boundary higher spin current exhibits singularities on both bulk and boundary light cones. We also comment on a possible extension to the level of three-point functions and carry out a causal construction for higher spin fields in de Sitter spacetime.