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 (γ-ωz^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.

27 pages, 19 figures. Accepted for publication in Phys. Rev. D

References in corpus (4)

• Domain wall brane in squared curvature gravity
• Bulk matter fields on two-field thick branes
• A Transfer Matrix Method for Resonances in Randall-Sundrum Models
• Exact solutions for a Maxwell-Kalb-Ramond action with dilaton: Localization of massless and massive modes in a sine-Gordon brane-world

Cited by in corpus (13)

• Heun Functions and Some of Their Applications in Physics
• Analytic results in the position-dependent mass Schrodinger problem
• Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials
• Energy eigenfunctions for position-dependent mass particles in a new class of molecular hamiltonians
• Kalb-Ramond excitations in a thick-brane scenario with dilaton
• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Approximative Analytic Study of Fermions in Magnetar's Crust; Ultra-relativistic Plane Waves, Heun and Mathieu Solutions and Beyond
• Symbolic analysis of second-order ordinary differential equations with polynomial coefficients
• Universal Mass Scale for Bosonic Fields in Multi-Brane Worlds
• Universal Mass Scale for Bosonic Fields in Multi-Brane Worlds
• The $d$-dimensional softcore Coulomb potential and the generalized confluent Heun equation
• Confluent Heun functions and the Coulomb problem for spin 1/2 particle in Minkowski space