Fractional and semi-local non-Abelian Chern-Simons vortices

TL;DR

This paper investigates fractional and semi-local non-Abelian Chern-Simons vortices in specific gauge theories, solving master equations numerically and analyzing flux structures and profiles.

Contribution

It introduces numerical solutions for fractional and semi-local Chern-Simons vortices in new gauge theories, revealing flux structure transitions and profile characteristics.

Findings

Fractional vortices exhibit non-rotational symmetry in the transverse plane.

Ring-like flux structures become bell-like unless vortex centers are coincident.

Effective sizes and asymptotic profiles of vortices are characterized.

Abstract

In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U(1) x SO(2M) and G = U(1) x USp(2M) theories. The master equations are solved numerically using appropriate Ansatze for the moduli matrix field. In the fractional case the vortices are solved in the transverse plane due to the broken axial symmetry of the configurations (i.e. they are non-rotational invariant). It is shown that unless the fractional vortex-centers are all coincident (i.e. local case) the ring-like flux structure, characteristic of Chern-Simons vortices, will become bell-like fluxes - just as those of the standard Yang-Mills vortices. The asymptotic profile functions are calculated in all cases and the effective size is identified.