Effective string theory for vortex lines in fluids and superfluids

TL;DR

This paper develops a comprehensive effective string theory framework for vortex lines in fluids and superfluids, incorporating bulk fluid flow via a two-form field and analyzing low-energy couplings and RG running.

Contribution

It generalizes previous models by deriving a broad low-energy effective Lagrangian for vortex lines, compatible with symmetries, and explores classical RG running of coupling constants.

Findings

Derived the most general low-energy effective Lagrangian for vortex lines.

Showed that certain coupling constants exhibit classical RG running.

Applied techniques to Kelvin waves, vortex rings, and sound mode coupling.

Abstract

We discuss the effective string theory of vortex lines in ordinary fluids and low-temperature superfluids, by describing the bulk fluid flow in terms of a two-form field to which vortex lines can couple. We derive the most general low-energy effective Lagrangian that is compatible with (spontaneously broken) Poincare invariance and worldsheet reparameterization invariance. This generalizes the effective action developed by Lund and Regge and by Endlich and Nicolis. By applying standard field-theoretical techniques, we show that certain low-energy coupling constants -- most notably the string tension -- exhibit RG running already at the classical level. We discuss applications of our techniques to the study of Kelvin waves, vortex rings, and the coupling to bulk sound modes.