The Euler current and relativistic parity odd transport

TL;DR

This paper introduces a new topological current related to the Euler characteristic in odd-dimensional spacetimes, enabling the formulation of relativistic effective theories for quantum Hall states and superfluids with novel transport properties.

Contribution

It presents a novel topological current tied to the Euler characteristic, leading to new Chern-Simons terms in effective field theories for quantum Hall and superfluid systems.

Findings

Defines a conserved topological current linked to the Euler characteristic.

Derives new Chern-Simons-type terms for relativistic quantum Hall and superfluid theories.

Identifies transport coefficients such as Hall viscosity in these systems.

Abstract

For a spacetime of odd dimensions endowed with a unit vector field, we introduce a new topological current that is identically conserved and whose charge is equal to the Euler character of the even dimensional spacelike foliations. The existence of this current allows us to introduce new Chern-Simons-type terms in the effective field theories describing relativistic quantum Hall states and (2+1) dimensional superfluids. Using effective field theory, we calculate various correlation functions and identify transport coefficients. In the quantum Hall case, this current provides the natural relativistic generalization of the Wen-Zee term, required to characterize the shift and Hall viscosity in quantum Hall systems. For the superfluid case this term is required to have nonzero Hall viscosity and to describe superfluids with non s-wave pairing.