Confluent Heun functions in gauge theories on thick braneworlds
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.
Keywords
Cite
@article{arxiv.1109.3486,
title = {Confluent Heun functions in gauge theories on thick braneworlds},
author = {M. S. Cunha and H. R. Christiansen},
journal= {arXiv preprint arXiv:1109.3486},
year = {2011}
}
Comments
27 pages, 19 figures. Accepted for publication in Phys. Rev. D