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.
Highlights
To provide necessary and sufficient conditions for a CFT to possess a local bulk dual [5,6,7]
Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality
The result may shed some light on the issue of bulk locality in higher-spin holography, and the present paper aims to prepare the technical tools for attacking the above concrete match
Summary
We work with fields defined on (d + 1)-dimensional Euclidean anti-de Sitter space which will be denoted in the sequel, with a slight but standard abuse of terminology, as AdSd+1.15 Euclidean anti-de Sitter space is nothing but another name for hyperbolic space It is often realised as the (d + 1)-dimensional Poincare ball, its d-dimensional conformal boundary ∂AdSd+1 is topologically a sphere Sd. As was first noted by Dirac [88, 89], in such a set up it is often useful to make the mutual SO (d + 1, 1) symmetry of AdSd+1 and its conformal boundary manifest, so that the consequential symmetry constraints are manifestly realised. By expressing fields on AdSd+1 and its conformal boundary in terms of SO (d + 1, 1)covariant fields defined in the ambient space, their SO (d + 1, 1) symmetry is made manifest
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