Localization of $U(1)$ gauge field by non-minimal coupling with gravity

TL;DR

This paper introduces a new non-minimal coupling approach to localize the $U(1)$ gauge field on Randall-Sundrum-like braneworlds, revealing a continuous mass spectrum with tachyonic modes and implications for brane models.

Contribution

It proposes a novel non-minimal coupling action for gauge-gravity interaction that affects localization and mass spectrum in braneworld scenarios.

Findings

Mass spectrum is continuous with no gap between zero and massive modes.

All massive modes are non-localized and tachyonic.

The approach applies to various asymptotically anti-de Sitter braneworlds.

Abstract

In this paper, we investigate the localization of the $U(1)$ gauge field on Randall-Sundrum-like braneworld models. The localization of the $U(1)$ gauge field is important because it plays a fundamental role in the branworld theories. To achieve the localization, we propose a novel action with a non-minimal coupling between the $U(1)$ gauge field and gravity. We find that the mass spectrum of the gauge field is continuous, without any gap between the zero-mass mode and the massive modes, and except for the zero-mass mode all the massive modes are not localized on the brane. Furthermore, the massive modes have negative squared masses, indicating they are tachyonic. Our analysis can be applied to a wide range of thin and thick braneworld scenarios, provided that the five-dimensional spacetime is asymptotically anti-de Sitter.