Comparison of two gauge-nonequivalent IAnsäItzeB for charged vortices in SU(2) gauge theory with Chern-Simons term

Abstract

We discuss in detail the possible connection between the two topologically equivalent but gauge-nonequivalent Ansa$uml-tze for charged (neutral) vortices in an SU(2) non-Abelian Higgs model with (without) a Chern-Simons term. In particular, we show that when the magnitude of the two Higgs fields are proportional to each other in the Ansatz where the global gauge group is SU(2) then the field equations and the energy functional in the two Ansa$uml-tze have identical form in terms of the corresponding dimensionless Ginzburg-Landau-type parameters η and λ. In this case we show that for a wide range of parameters the charged (as well as neutral) one-vortex energy in the Ansatz, in which the fields are in the adjoint representation of SU(2) so that the global gauge group is SU(2)/Z₂, is less than the corresponding energy in the Ansatz where the global gauge group is SU(2). For the neutral case we also obtain an exact and approximate analytic one-vortex solution in case λ=1 and 2, respectively (and η=1). Finally we show that charged (as well as neutral) Z₃ vortices of the SU(3) gauge theory repel each other in the dominant part of the type-II region of superconductivity (i.e., λ>η).