Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation

TL;DR

We develop a dual gauge theory for 2D Galilean-invariant conventional and chiral superfluids at zero temperature, emphasizing general coordinate invariance and a gauge-duality framework that maps density and velocity to a dual gauge field. The construction leverages a Wen-Zee term to encode parity-violating effects such as edge currents and Hall viscosity, and uses a Newton-Cartan formulation to access covariant currents and energy flow. We show that the chiral NR superfluid arises as the nonrelativistic limit of a relativistic Euler-current theory, with the Wen-Zee coupling recovered in the NR limit via $s=-\kappa/(4\pi)$. A covariant NC action for both conventional and chiral superfluids is developed, enabling systematic computation of energy currents and highlighting how geometry sources modify parity-violating responses. The framework sets the stage for covariant descriptions of chiral superconductors and topological edge physics in nonrelativistic fluids.

Abstract

We present a theory of Galilean-invariant conventional and chiral $p_x \pm ip_y$ fermionic superfluids at zero temperature in two spatial dimensions in terms of a dual gauge theory. Our formulation is general coordinate invariant. The parity-violating effects are encoded in the Wen-Zee term that gives rise to the Hall viscosity and edge current. We show that the relativistic superfluid with the Euler current reduces to the chiral superfluid in the limit $c\to\infty$. Using Newton-Cartan geometry we construct the covariant formulation of the effective theory and calculate the energy current.