Non-Abelian vortex lattices

TL;DR

This paper numerically explores the phase diagram of a model with non-Abelian vortices, revealing conditions for vortex lattice formation and their internal moduli behavior.

Contribution

It provides the first detailed numerical analysis of non-Abelian vortex lattice structures and their phase transitions in a specific theoretical model.

Findings

Vortex lattices form in certain parameter regions.

At large spacing, low energy theory reduces to multiple CP(1) models.

Smaller spacing leads to a unified internal rotation mode.

Abstract

We perform a numerical study of the phase diagram of the model proposed in \cite{Shifman:2012vv}, which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of $CP(1)$ theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.