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

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