Exact solutions for a Maxwell-Kalb-Ramond action with dilaton: Localization of massless and massive modes in a sine-Gordon brane-world

TL;DR

This paper analytically derives the exact propagation modes of electromagnetic and Kalb-Ramond fields in a five-dimensional brane-world with a dilaton, revealing conditions for localization, mass spectra, and suppression of massive modes in four dimensions.

Contribution

It provides exact solutions for gauge field modes in a dilaton-coupled brane-world, including a quantization condition and criteria to avoid tachyons, advancing understanding of field localization.

Findings

Exact zero-mode and massive mode solutions for gauge fields

Quantization condition for the mass spectrum depending on dilaton coupling

Suppression of Kaluza-Klein massive modes in 4D physics

Abstract

We analytically find the exact propagation modes of the electromagnetic and the Kalb-Ramond fields together in a five-dimensional curved space-time. The existence and localization of gauge particles into our four-dimensional world (4D) is studied in detail on a brane-world scenario in which two gauge fields interact with a dilaton and a gravitational background. The coupling to the dilaton is different in each case causing the splitting between both gauge spectra. The gauge field zero-modes and an infinite tower of Kaluza-Klein massive states are analytically obtained. Relevant conditions on the dilaton coupling constant are found in order to identify with precision every finite tensor and vector eigenstate in the theory. An exact quantization condition on the whole mass spectrum, depending on the dilaton coupling constant and the bulk Planck mass, is inherited from the extra-dimension. This allows finding an exact rule to prevent tachyons in the theory and, by the same token, predicting a possible Kalb-Ramond tensor zero-mode in 4D world. We also show that KK massive-modes contributions onto 4D physics are strongly suppressed.