Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange

TL;DR

This paper computes higher-spin gauge boson exchange contributions to four-point functions in AdS/CFT, deriving bulk-to-bulk propagators and expressing exchanges as conformal partial waves, advancing holographic bulk interaction understanding.

Contribution

It provides the first complete bulk-to-bulk propagators for massless higher-spin fields in various gauges and dimensions, facilitating holographic reconstruction of bulk interactions.

Findings

Derived explicit bulk-to-bulk propagators for higher-spin fields.

Expressed higher-spin exchanges as conformal partial waves.

Progressed towards understanding bulk locality in holography.

Abstract

Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in $AdS_{d+1}$ to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality.