Topological Landau-Ginzburg Theory for Vortices in Superfluid $^4$He

TL;DR

This paper introduces a novel topological Landau-Ginzburg framework for modeling vortex dynamics in superfluid helium-4, incorporating gauge fields and topological terms to capture vortex behavior and Berry phase effects.

Contribution

It develops a new topological Landau-Ginzburg theory with gauge fields for vortex strings in superfluid helium-4, highlighting the role of topological terms in vortex dynamics.

Findings

Inclusion of gauge fields removes singularities in the superfluid order parameter.

The theory naturally incorporates Berry phase effects in vortex motion.

Provides a comprehensive description of vortex dynamics in superfluid helium-4.

Abstract

We propose a new Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid $^4$He. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.