Domain Wall Solution Arising in Abelian Higgs Model Subject to Born-Infeld Theory of Electrodynamics

TL;DR

This paper investigates domain wall solutions in the Abelian Higgs model coupled with Born-Infeld electrodynamics, demonstrating existence, uniqueness, and asymptotic behavior of solutions under specific boundary conditions.

Contribution

It introduces a reduction of BPS equations to a quasi-linear differential equation and establishes the existence and uniqueness of solutions with detailed asymptotic analysis.

Findings

Unique solution exists under specified boundary conditions.

Solution exhibits a phase transition behavior.

Asymptotic estimates at infinity are derived.

Abstract

In this note we research the Abelian Higgs model subject to the Born-Infeld theory of electrodynamics for which the BPS equations can be reduced into a quasi-linear differential equation. We show that the equation exists a unique solution under two interesting boundary conditions which realize the corresponding phase transition. We construct the solution through a dynamical shooting method for which the correct shooting slope is unique. We also obtain the sharp asymptotic estimate for the solution at infinity.