Bogomol'nyi equations in gauge theories

摘要

By imposing self-duality conditions, we obtain the explicit form in whichgauge theories spontaneously breakdown in the Bogomol'nyi limit. In thiscontext, we reconsider the Abelian Higgs, Chern-Simons Higgs andMaxwell-Chern-Simons Higgs models. On the same footing, we find a topologicalHiggs potential for a Maxwell-Chern-Simons extended theory presenting bothminimal and nonminimal coupling. Finally, we perform a numerical calculation inthe asymmetric phase and show the solutions to the self-dual equations ofmotion of the topological theory. We argue about certain relations among theparameters of the model in order to obtain such vortex configurations.