Covariant effective action for a Galilean invariant quantum Hall system

TL;DR

This paper develops a covariant effective field theory for gapped quantum Hall systems in curved Galilean backgrounds, enabling a unified analysis of various currents and extending previous models to arbitrary order.

Contribution

It introduces a covariant effective action framework for Galilean invariant quantum Hall systems coupled to complex background geometries, including torsion and gravitational effects.

Findings

Unified description of charge, energy, stress, and mass currents.

Extension of Hoyos and Son's improvement terms to all orders in mass.

Framework accommodates curved spacetimes with torsion and gravity.

Abstract

We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son's improvement terms to arbitrary order in $m$.