Stabilizing textures with magnetic fields

TL;DR

This paper explores how magnetic fields can stabilize textures in field theories, especially through gauge fields and modifications to the scalar field coupling, with a focus on U(1) gauge groups in two and three dimensions.

Contribution

It demonstrates that modifying the scalar field coupling can stabilize textures via gauge fields, and connects gauge field dynamics to Skyrme-like models in certain limits.

Findings

Gauge fields can stabilize textures with modified scalar couplings.

In the U(1) case, the system reduces to a Skyrme-like model under certain conditions.

Non-abelian textures remain unstable; no stabilization examples are known.

Abstract

The best-known way of stabilizing textures is by Skyrme-like terms, but another possibility is to use gauge fields. The semilocal vortex may be viewed as an example of this, in two spatial dimensions. In three dimensions, however, the idea (in its simplest form) does not work -- the link between the gauge field and the scalar field is not strong enough to prevent the texture from collapsing. Modifying the |D Phi|^2 term in the Lagrangian (essentially by changing the metric on the Phi-space) can strengthen this link, and lead to stability. Furthermore, there is a limit in which the gauge field is entirely determined in terms of the scalar field, and the system reduces to a pure Skyrme-like one. This is described for gauge group U(1), in dimensions two and three. The non-abelian version is discussed briefly, but as yet no examples of texture stabilization are known in this case.