Non-commutative effective field theory of the lowest Landau level superfluid

TL;DR

This paper derives a microscopic effective field theory for a rotating superfluid's vortex excitations, revealing their non-commutative nature and providing quantitative predictions relevant to Bose-Einstein condensate experiments.

Contribution

It introduces a novel derivation of the effective field theory using a lowest Landau level projected coherent state path integral approach, clarifying the microscopic origin of non-commutative fields.

Findings

Provides a microscopic derivation of the non-commutative effective field theory.

Makes quantitative predictions for low-energy behavior based on microscopic parameters.

Connects theoretical predictions with trapped Bose-Einstein condensate experiments.

Abstract

A 2+1D superfluid in a rapidly rotating trap forms an array of vortices, with collective excitations called Tkachenko modes. Du et al. (2024) argued from an effective field theory viewpoint that these excitations are described by a field theory living on a non-commutative space. We elucidate the microscopic origin of these non-commutative fields, and present a novel derivation of the effective field theory for this superfluid using a lowest Landau level projected coherent state path integral approach. Besides conceptual clarity, this approach makes quantitative predictions about the long-wavelength, low-energy behavior in terms of the microscopic parameters of the short-range interacting lowest Landau level superfluid -- relevant to trapped Bose-Einstein condensate experiments.