Self-dual configurations in Abelian Higgs models with $k$-generalized gauge field dynamics

TL;DR

This paper demonstrates the existence of self-dual vortex solutions in generalized Maxwell-Higgs models with nonlinear gauge field dynamics, revealing new features in vortex behavior and properties.

Contribution

It introduces a class of $k$-generalized models with nonlinear gauge kinetic terms supporting self-dual solutions, expanding the understanding of vortex configurations in such theories.

Findings

Existence of self-dual solutions with nonlinear gauge dynamics.

Vortex solutions exhibit exponential or power-law decay depending on the potential.

Generalization affects vortex core size, magnetic field, and bosonic masses, but not total energy.

Abstract

We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a $k$-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of $F_{\mu\nu}F^{\mu\nu}$. We have implemented our proposal by means of a $k$-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of $k$-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with $|\phi|^4$-potential or $|\phi |^6$-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the $k$-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.