Self-Dual Effective Compact and True Compacton Configurations in Generalized Abelian Higgs Models

Abstract

We have studied the existence of self-dual effective compact and true compacton configurations in Abelian Higgs models withgeneralized dynamics. We have named an effective compact solution the one whose profile behavior is very similar to the one ofa compacton structure but still preserves a tail in its asymptotic decay. In particular, we have investigated the electrically neutralconfigurations of the Maxwell-Higgs and Born-Infeld-Higgs models and the electrically charged ones of the Chern-Simons-Higgsand Maxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms is performed by means of dielectric functions ingauge and Higgs sectors. The implementation of the BPS formalism without the need to use a specificAnsatzhas led us to the explicitdetermination for the dielectric function associated with the Higgs sector to be proportional to𝜆|𝜙|2𝜆−2,𝜆>1. Consequently, thefollowed procedure allows us to determine explicitly new families of self-dual potential for every model. We have also observedthat, for sufficiently large values of𝜆, every model supports effective compact vortices. The true compacton solutions arising for𝜆=∞are analytical. Therefore, these new self-dual structures enhance the space of BPS solutions of the Abelian Higgs modelsand they probably will imply interesting applications in physics and mathematics.