Exact Solutions of Multi-Vortices and False Vacuum Bubbles in Noncommutative Abelian-Higgs Theories

TL;DR

This paper constructs exact multi-vortex and false vacuum bubble solutions in noncommutative Abelian-Higgs theories, revealing new solutions beyond BPS states and analyzing their stability.

Contribution

It introduces novel exact solutions for multi-vortices and false vacuum bubbles in noncommutative Abelian-Higgs models, including cases not satisfying BPS equations.

Findings

Exact multi-vortex solutions that do not follow BPS equations.

Construction of false vacuum bubble solutions with magnetic flux.

Discussion of classical stability of the solutions.

Abstract

We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.