Dual Gauge Theory for Two Dimensional Superfluid Turbulence

Can turbulent hydrodynamics in two-dimensional superfluids be described through a dual gauge theory framework, and how does this dual formulation capture phenomena such as the kinetic energy cascade and vortex clustering?

The authors formulate a dual gauge theory for two-dimensional superfluids by coupling point-like vortices to an emergent 2+1-dimensional U(1) gauge field, where superfluid velocity and density map to dual electric and magnetic fields. They numerically evolve the resulting non-relativistic, non-linear equations of motion in the presence of stochastic vortex pair production, dipole annihilation, and thermal friction.

Simulations of the dual equations of motion reveal a turbulent steady state that exhibits an incompressible kinetic energy spectrum consistent with Kolmogorov's (k^{-5/3}) scaling law at wavenumbers below the forcing scale. Furthermore, the observation of vortex clustering and the analysis of conservative energy transfer fluxes confirm the presence of an inverse energy cascade, where incompressible kinetic energy is transferred toward smaller wavenumbers.

This dual gauge theory provides a novel collective-variable perspective on superfluid turbulence, bridging the microscopic dynamics of topological defects (quantized vortices) with macroscopic hydrodynamical scaling laws usually studied in classical fluid dynamics.