Graviton and gauge boson propagators in AdS(d+1)

TL;DR

This paper constructs gauge field and graviton propagators in Euclidean AdS(d+1) space using two methods, confirming the gauge-invariant parts match, and providing explicit elementary function expressions.

Contribution

It introduces two distinct methods for deriving propagators in AdS space, validating their gauge-invariant components and offering explicit solutions.

Findings

Gauge-invariant propagators are consistent across methods.

Explicit elementary function expressions for propagators are obtained.

Both physical and gauge parts of propagators are determined.

Abstract

We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the propagators which reflect their gauge structure. This leads to a rapid determination of the physical part of the propagators in terms of elementary functions. The second method is a more traditional approach using covariant gauge fixing which leads to a solution for both physical and gauge parts of the propagators. The gauge invariant parts agree in both methods.