Boundary Conditions and Dualities: Vector Fields in AdS/CFT

TL;DR

Marolf and Ross extend the AdS/CFT dictionary from scalars to vector fields by classifying admissible, finite, conserved boundary conditions via Ishibashi–Wald results. They show that general linear boundary conditions correspond to multi-trace deformations in the dual CFT, triggering RG flows between UV and IR fixed points, with the vector case exhibiting distinctive features due to gauge invariance and the nature of F^I and A_I operators. In particular, for AdS4/CFT3 the dual of the bulk photon can be a propagating gauge field in the CFT, and the authors discuss hybrid boundary conditions that break Lorentz invariance in the UV but restore it in the IR, as well as potential tensor-field generalizations suggesting a link between AdS4 string theory and 3D quantum gravity. The work provides a unified, dimension-dependent treatment of vector boundary conditions, highlights the emergence of non-local or gauge-field duals, and outlines a broad landscape of new holographic dualities and stability considerations.

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.