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

TL;DR

This paper develops a gauge-theoretic and geometric framework for two-dimensional chiral superfluids, capturing their topological and parity-violating properties, and connects relativistic and non-relativistic descriptions.

Contribution

It introduces a dual gauge theory and Newton-Cartan formulation for chiral superfluids, providing a covariant and coordinate-invariant effective theory that includes Hall viscosity and edge effects.

Findings

Derived the effective theory incorporating Wen-Zee term

Connected relativistic and non-relativistic superfluid descriptions

Calculated the energy current in the Newton-Cartan framework

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.