(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the \nu=1/2 state

TL;DR

This paper develops a unified theoretical framework for the quantum Hall effect, reconciling localization, topological aspects, and Coulomb interactions, and introduces a new symmetry called F-invariance with implications for electromagnetic response.

Contribution

It introduces a unifying theory that combines different approaches to the quantum Hall effect and identifies a new symmetry, F-invariance, with broad physical consequences.

Findings

F-invariance symmetry has significant physical implications.

Response calculations are consistent only when F-invariance is maintained.

The theory applies to both integer and fractional quantum Hall regimes.

Abstract

We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and Chern-Simons gauge theory. We elaborate on the microscopic origins of the effective action and unravel a new symmetry in the problem with Coulomb interactions which we name F-invariance. This symmetry has a broad range of physical consequences which will be the main topic of future analyses. In the second half of this paper we compute the response of the theory to electromagnetic perturbations at a tree level approximation. This is applicable to the theory of ordinary metals as well as the composite fermion approach to the half-integer effect. Fluctuations in the Chern-Simons gauge fields are found to be well behaved only when the theory is F-invariant.