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

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 $|\varphi {|}^4$-potential or $|\varphi {|}^6$-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.

11 pages, Latex 2e, 12 figures; major revision

References in corpus (8)

• k-defects as compactons
• Cosmic Strings and Cosmic Superstrings
• K fields, compactons, and thick branes
• Bogomol'nyi Equations for Vortices in Born-Infeld-Higgs Systems
• Localized D-dimensional global k-defects
• Topological vortices in generalized Born-Infeld-Higgs electrodynamics
• Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
• Analytical BPS Maxwell-Higgs vortices

Cited by in corpus (7)

• Twinlike Models for Kinks, Vortices and Monopoles
• Self-dual solitons in a generalized Chern-Simons baby Skyrme model
• Long range vortex configurations in generalized models with the Maxwell or Chern-Simons dynamics
• Self-dual solitons in a Maxwell-Chern-Simons baby Skyrme model
• Vortices in a generalized Maxwell-Higgs model with visible and hidden sectors
• Self-dual solitons in a Born-Infeld baby Skyrme model
• First order framework for gauge k-vortices