Holographic representation of bulk fields with spin in AdS/CFT

TL;DR

This paper constructs holographic representations of bulk fields with spin in AdS/CFT, demonstrating how to recover bulk gauge fields and metric fluctuations from boundary data while maintaining covariance and locality.

Contribution

It provides explicit smearing functions for spin-1 and spin-2 fields in AdS, extending holographic reconstruction techniques to include gauge fields and gravitons.

Findings

Bulk two-point functions respect locality.

Representation maintains AdS covariance with gauge transformations.

Includes methods for interacting massive vectors in 1/N expansion.

Abstract

We develop the representation of bulk fields with spin one and spin two in anti-de Sitter space, as non-local observables in the dual CFT. Working in holographic gauge in the bulk, at leading order in 1/N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1/N perturbation theory, and we comment on the issue of general backgrounds.