Covariant Graviton Propagator in Anti-de Sitter Spacetime

TL;DR

This paper derives the covariant graviton propagator in n-dimensional anti-de Sitter spacetime, analyzing its gauge dependence and revealing complex hypergeometric function terms in most gauges, using Euclidean methods.

Contribution

It provides the most general covariant gauge construction of the graviton propagator in AdS spacetime and examines its behavior across different gauge parameters.

Findings

Propagator contains complex hypergeometric functions in most gauges.

Landau gauge simplifies the propagator structure.

Euclidean approach is used for calculations.

Abstract

We construct the graviton propagator in $n$-dimensional anti-de Sitter spacetime in the most general covariant gauge. We then study the behaviour of this propagator for different values of the gauge parameters. We will show that in any gauge, apart from the Landau gauge, the graviton propagator in the AdS spacetime contains a complicated term involving the derivative of a hypergeometric function which can not be expressed in terms of elementary functions. We do our calculations in the Euclidean approach.