Noncommutative effective field theory of the lowest Landau level superfluid

A (2+1) -dimensional superfluid in a rapidly rotating trap forms an array of vortices, with collective excitations called Tkachenko modes. Du et al. Phys. Rev. Res. 6, L012040 (2024) argued from an effective field theory viewpoint that these excitations are described by a field theory living on a noncommutative space. We elucidate the microscopic origin of these noncommutative fields, and present a derivation of the effective field theory for this superfluid using a lowest Landau level projected coherent state path-integral approach. Aside from 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.