Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector

TL;DR

This paper investigates fermion zero modes in a 2+1 dimensional Chern-Simons-Higgs model with visible and hidden sectors, revealing how vortex configurations influence zero mode count and fermion number violation.

Contribution

It introduces a model with coupled visible and hidden sectors and demonstrates how vortex numbers determine fermionic zero modes through a fine-tuning approach.

Findings

Number of fermionic zero modes equals the absolute sum of vortex numbers in both sectors.

Fermion number violation occurs due to specific interaction terms.

Zero mode count can be controlled via fine-tuning of model parameters.

Abstract

In this paper we study a $2+1$ dimensional system in which fermions are coupled to the self-dual topological vortex in $U(1) \times U(1)$ Chern-Simons theory, where both $U(1)$ gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.