How often does the Unruh-DeWitt detector click beyond four dimensions?

TL;DR

This paper investigates the response of an Unruh-DeWitt detector in higher-dimensional Minkowski spacetimes, revealing divergences in transition probabilities and rates beyond certain dimensions, which impacts the applicability of GEMS methods.

Contribution

It provides a detailed analysis of the detector's response in up to six dimensions, highlighting the divergence behavior and limitations of GEMS in higher dimensions.

Findings

Transition probability diverges in dimensions >3 in the sharp switching limit.

Transition rate remains finite up to dimension 5 for constant acceleration trajectories.

In 6D, the transition rate diverges for generic trajectories, limiting GEMS applicability.

Abstract

We analyse the response of an arbitrarily-accelerated Unruh-DeWitt detector coupled to a massless scalar field in Minkowski spacetimes of dimensions up to six, working within first-order perturbation theory and assuming a smooth switch-on and switch-off. We express the total transition probability as a manifestly finite and regulator-free integral formula. In the sharp switching limit, the transition probability diverges in dimensions greater than three but the transition rate remains finite up to dimension five. In dimension six, the transition rate remains finite in the sharp switching limit for trajectories of constant scalar proper acceleration, including all stationary trajectories, but it diverges for generic trajectories. The divergence of the transition rate in six dimensions suggests that global embedding spacetime (GEMS) methods for investigating detector response in curved spacetime may have limited validity for generic trajectories when the embedding spacetime has dimension higher than five.