Bulk-to-bulk photon propagator in AdS

TL;DR

This paper analyzes the photon bulk-to-bulk propagator in AdS space across various gauges, providing new expressions and insights into gauge invariance and IR behavior.

Contribution

It introduces new formulations of the propagator in different gauges and clarifies gauge invariance and IR properties in AdS.

Findings

Derived explicit propagator expressions in axial, Coulomb, and covariant gauges.

Showed the propagator's IR behavior improves in Fried-Yennie gauge.

Connected gauge invariance conditions to ghost propagators.

Abstract

We study the photon bulk-to-bulk propagator in AdS in various gauges, including axial, Coulomb, and the standard covariant gauge. We compute the propagator using both momentum and position space techniques. We ensure the propagators obtained obey the right subsidiary conditions arising from gauge invariance. In particular, BRST invariance implies a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator. Our method relies on decomposing the components of the propagator in terms of independent tensor structures and solving for the form factors. We recover some previously existing results and obtain new expressions for the propagator in other gauges. The propagator in axial and Coulomb gauge is simpler in momentum space, as momentum space makes manisfest the translational invariance in the boundary directions, while the position space expression is the simplest in the covariant Fried-Yennie gauge. In this gauge the propagator has an improved IR behavior, somewhat analogous to the UV improved behavior associated with the Landau gauge in flat space. The results readily extend to Yang-Mills fields.