Quantum vorticity: a not so effective field theory

TL;DR

This work analyzes the quantum formulation of the classical perfect fluid, revealing an infinite-dimensional symmetry that causes vanishing transverse dispersion at the classical level and induces UV/IR mixing in the quantum theory. By studying two inequivalent Lagrangian descriptions (comoving and Clebsch), the authors show that, while the energy spectra agree, the quantum Hilbert spaces differ, yielding an infinite tower of degenerate vorton states with a quadratic dispersion $\omega \propto \mathbf{k}^2$ and an unusually strong dependence on UV physics. A lattice (SU(N)) regularization is constructed to preserve a deformed version of the symmetry, and a matrix-model realization clarifies how continuum results emerge for low momenta. The findings illuminate a novel universality class for quantum fluids, connect to fracton-like UV/IR phenomena, and motivate potential but challenging routes to experimental realization via nonlocal lattice constructs and 2D analogues like positronium. Overall, the paper establishes a coherent quantum framework for incompressible fluids with rich symmetry structures and paves the way for further exploration of vorton dynamics and their physical implications.

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 $(ρ, p, u^μ)$ 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 $ω= 0$ 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 $ω\propto \mathbf{k}^2$, 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.

Figures (1)

• Figure 1: Diagrammatic representation of the scattering amplitude of two positronium in the t-channel up to second order in the Born approximation.