Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes

Abstract

Abstract:In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged U(1) nonlinear CP 1 -model. If 2πn, n ∈ Z, is the quantized magnetic flux of the two species of BPS vortex solutions, 2n linearly-independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension 2n of these stringy topological defects is thus locally shown.

SUSY Chern–Simons $\mathbb{CP}^N$ and baby Skyrme models and their BPS structures

“…We will show how to construct an 'universal' set of BPS equations for gauge theories in three dimensions and provide a method to determine the BPS-type of the solutions. Then, we apply these ideas to different gauged CP N models and compare our results, naturally obtained from SUSY, with previous results found in the literature [20][21][22][23][24][25][26][27][28][29][30][31]. This formulation provides an explanation, in terms of supersymmetry, to the presence (absence) of self-dual structure in some models.…”

“…Then, we apply these ideas to different gauged CP N models and compare our results, naturally obtained from SUSY, with previous results found in the literature. The gauged CP N models, specially the CP 1 and CP 2 models, were treated previously regarding their BPS structure [21][22][23][24][25][26][27], their SUSY solutions [28,29] or some generalized BPS models [30][31][32]. We will construct an N = 2 extension for the gauge formulation of the gauge CP N models with Chern-Simons term.…”