https://doi.org/10.1140/epjc/s10052-025-13769-y
Regular Article - Theoretical Physics
Propagators in AdS for higher-derivative and nonlocal gravity: Heat kernel approach
1
Faculty of Mathematics and Physics, Institute of Theoretical Physics, Charles University, V Holešovičkách 2, 180 00, Prague, Czech Republic
2
Van Swinderen Institute, University of Groningen, 9747 AG, Groningen, Netherlands
3
Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czech Republic
Received:
4
December
2023
Accepted:
30
December
2024
Published online:
10
February
2025
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 
dimensions.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
