Boundary Conditions and Dualities: Vector Fields in AdS/CFT

TL;DR

This paper explores how boundary conditions for vector fields in AdS space influence dual field theories, revealing new gauge/gravity dualities and the potential for novel quantum gravity correspondences in three dimensions.

Contribution

It extends the analysis of boundary conditions from scalar to vector fields in AdS/CFT, uncovering new dualities and RG flows involving gauge fields.

Findings

Boundary conditions for vector fields induce multi-trace deformations.

These deformations lead to renormalization-group flows in dual theories.

In AdS4/CFT3, the dual of the bulk photon is a propagating gauge field.

Abstract

In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the bulk spacetime using the results of Ishibashi and Wald [hep-th/0402184]. As in the context of scalar fields, general boundary conditions for vector fields involve multi-trace deformations which lead to renormalization-group flows. Such flows originate in ultra-violet CFTs which give new gauge/gravity dualities. At least for AdS4/CFT3, the dual of the bulk photon appears to be a propagating gauge field instead of the usual R-charge current. Applying similar reasoning to tensor fields suggests the existence of a duality between string theory on AdS4 and a quantum gravity theory in three dimensions.