Some exact BPS solutions for exotic vortices and monopoles

TL;DR

This paper provides new analytical BPS solutions for vortices and monopoles in generalized gauge theories, extending previous solutions and exploring higher winding numbers with specific scalar-field-dependent functions.

Contribution

It introduces new exact BPS solutions in generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, including higher winding vortices with specific scalar functions.

Findings

New analytical solutions for BPS vortices and monopoles.

Extension of previous solutions to higher winding numbers.

Solutions with scalar functions that ensure positive energy density.

Abstract

We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in \cite{Casana:2014qfa, Casana:2013lna}. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, $f(|\phi|)$ and $w(|\phi|)$. For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize that of exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that $w(|\phi|)$ has negative value at some finite range of $r$, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.