Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect

TL;DR

This paper introduces an extended Nappi-Witten geometric model for the fractional quantum Hall effect, unifying gauge, gravitational, and edge state descriptions within a Chern-Simons framework.

Contribution

It presents a novel non-relativistic geometric approach that extends Nappi-Witten geometry to describe fractional quantum Hall states and their edge excitations.

Findings

Unified Chern-Simons description of Hall conductance and viscosity

Derivation of edge chiral boson from boundary Wess-Zumino-Witten model

Extension of Nappi-Witten algebra to non-relativistic quantum Hall geometry

Abstract

Motivated by the recent progresses in the formulation of geometric theories for the fractional quantum Hall states, we propose a novel non-relativistic geometric model for the Laughlin states based on an extension of the Nappi-Witten geometry. We show that the U(1) gauge sector responsible for the fractional Hall conductance, the gravitational Chern-Simons action and Wen-Zee term associated to the Hall viscosity can be derived from a single Chern-Simons theory with a gauge connection that takes values in the extended Nappi-Witten algebra. We then provide a new derivation of the chiral boson associated to the gapless edge states from the Wess-Zumino-Witten model that is induced by the Chern-Simons theory on the boundary.