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

TL;DR

The paper develops two covariant schemes to compute gauge boson and graviton propagators in Euclidean $AdS_{d+1}$, separating gauge artifacts from physical content. A rapid bitensor-based method yields gauge-invariant functions $F(u)$, $G(u)$, and $H(u)$ without gauge fixing, while a complementary Landau-gauge approach reproduces the same physical parts and provides explicit expressions via hypergeometric and elementary functions. The two methods are shown to be equivalent on the physical sector, enabling clean AdS/CFT applications such as 4-point correlators by focusing on gauge-invariant propagation. The results furnish explicit, tractable propagators in arbitrary dimensions, with detailed forms for even/odd $d$ and concrete checks in $n=d+1=5$ cases.

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.