Propagators in AdS for higher-derivative and nonlocal gravity: Heat kernel approach

TL;DR

This paper introduces a covariant heat kernel method to construct propagators in AdS space for various gravitational theories, including higher-derivative and nonlocal models, providing explicit formulas and correcting previous derivations.

Contribution

It develops a unified heat kernel approach to derive propagators in AdS for a broad class of gravitational theories, including higher-derivative and nonlocal models, with explicit constructions and corrections.

Findings

Explicit heat kernel expressions for scalar and tensor propagators in AdS.

Unified covariant method applicable to various gravity theories.

Corrected derivation of the quadratic action in arbitrary dimensions.

Abstract

We present a new covariant method of construction of the (position space) propagators in the $N$-dimensional (Euclidean) anti-de Sitter background for any gravitational theory with the Lagrangian that is an analytic expression in the metric, curvature, and covariant derivative. We show that the propagators (in Landau gauge) for all such theories can be expressed using the heat kernels for scalars and symmetric transverse-traceless rank-2 tensors on the hyperbolic $N$-space. The latter heat kernels are constructed explicitly and shown to be directly related to the former if an improved bi-scalar representation is used. Our heat kernel approach is first tested on general relativity, where we find equivalent forms of the propagators. Then it is used to obtain explicit expressions for propagators for various higher-derivative as well as infinite-derivative/nonlocal theories of gravity. As a by-product, we also provide a new derivation of the equivalent action (correcting a mistake in the original derivation) and an extension of the quadratic action to arbitrary ${N\geq 3}$ dimensions.