Confluent Heun functions in gauge theories on thick braneworlds

TL;DR

This paper analyzes gauge field propagation in a thick braneworld model using confluent Heun functions, deriving analytical solutions and examining Kaluza-Klein mode spectra in a Randall-Sundrum scenario.

Contribution

It introduces a novel analytical approach using confluent Heun functions to solve gauge field equations in thick braneworlds, providing explicit spectra and mode analysis.

Findings

Derived an analytical spectrum of gauge fields in the model

Established a connection between gauge field equations and confluent Heun functions

Analyzed the spectrum and weights of Kaluza-Klein modes

Abstract

We investigate the propagation modes of gauge fields in an infinite Randall-Sundrum scenario. In this model a sine-Gordon soliton represents our thick four-dimensional braneworld while an exponentially coupled scalar acts for the dilaton field. For the gauge-field motion we find a differential equation which can be transformed into a confluent Heun equation. By means of another change of variables we obtain a related Schrodinger equation with a family of symmetric rational (\gamma-\omega z^2)/(1-z^2)^2 potential functions. We discuss both results and present the infinite spectrum of analytical solutions for the gauge field. Finally, we assess the existence and the relative weights of Kaluza-Klein modes in the present setup.