Fractional quantum Hall effect in higher dimensions

TL;DR

This paper extends the fractional quantum Hall effect to higher dimensions by constructing an effective action using advanced mathematical tools, revealing new insights into topological states and their transport properties.

Contribution

It introduces a higher-dimensional fractional quantum Hall effective action based on a generalized parton picture and anomaly cancellation, expanding the theoretical framework of topological quantum states.

Findings

Derived the effective action for higher-dimensional fractional quantum Hall states.

Provided formulas for transport coefficients like Hall conductivity and viscosity.

Highlighted subtleties in anomaly cancellation in higher dimensions.

Abstract

Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the parton picture used in two spatial dimensions, the crucial ingredient being the cancellation of anomalies for the gauge fields binding the partons together. Some subtleties which exist even in two dimensions are pointed out. The effective action is obtained from a combination of the Dolbeault and Dirac index theorems. We also present expressions for some transport coefficients such as Hall conductivity and Hall viscosity for the fractional states.