Quantum vorticity: a not so effective field theory

TL;DR

This paper explores the formulation of quantum perfect fluids using effective field theory, revealing how quantum effects modify vortex excitations and discussing the challenges of maintaining symmetries in the quantum regime.

Contribution

It introduces multiple formulations of quantum fluid theories, analyzes UV-IR mixing effects, and proposes a lattice regularization preserving a deformed symmetry.

Findings

Quantum effects modify vortex dispersion to rac{f k}^2

Infinite degeneracy of quantum excitations

Lattice regularization preserves deformed symmetry

Abstract

We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(\rho, p, u^\mu)$ into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation $\omega = 0$ for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become $\omega \propto \mathbf{k}^2$, where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.