Accelerated paths and Unruh effect I: scalars and fermions in Anti De Sitter spacetime

TL;DR

This paper explores the Unruh effect in Anti de-Sitter spacetime by deriving exact detector response functions for scalars and fermions, revealing relationships between different couplings and spacetime dimensions.

Contribution

It provides exact expressions for the Unruh-DeWitt detector response in AdS spacetime for both scalar and fermionic fields, including quadratic coupling effects and dimensional relationships.

Findings

Exact response function for scalar fields in even-dimensional AdS.

Response of quadratic coupled fermionic detector proportional to scalar detector in doubled dimension.

Discussion on extending results to more general stationary motions.

Abstract

We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration. An exact expression of the detector response function for the scalar field has been obtained with different levels of non-linearity in even dimensional AdS spacetime. We also showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in $D$ dimensional $(D \geq 2)$ AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in $2D$ dimensional AdS spacetime. Here, the fermionic and scalar matter field is coupled minimally and conformally to the background AdS metric, respectively. Finally, we discuss about the extension of the results for more general stationary motion.