Higgs phase in a gauge $\mathbf{U}(1)$ non-linear $\mathbf{CP}^1$-model. Two species of BPS vortices and their zero modes

TL;DR

This paper analyzes zero modes around two types of BPS vortices in a critical Higgs phase of a gauged U(1) nonlinear CP^1 model, revealing two moduli spaces of vortex solutions with specific zero modes.

Contribution

It identifies and describes two species of BPS vortices and their zero modes, demonstrating the existence of two moduli spaces of dimension 2n for these topological defects.

Findings

Each vortex species has 2n linearly independent zero modes.

Two moduli spaces of dimension 2n are shown to exist.

Zero modes are explicitly described for both vortex species.

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 $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, 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.