Effective field theory description of the higher dimensional quantum Hall liquid

TL;DR

This paper develops an effective topological field theory for the four-dimensional quantum Hall liquid, describing its topological excitations and interactions, extending the understanding of higher-dimensional quantum Hall states.

Contribution

It introduces a novel effective field theory model for the 4D quantum Hall liquid, utilizing generalized flux attachment and describing topological excitations and interactions.

Findings

Formulates a U(1) Chern-Simons theory over $CP_3$

Describes topological excitations including particles, membranes, and 4-branes

Identifies a topological phase interaction among membranes

Abstract

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern-Simons theory over the total configuration space $CP_3$, or as a SU(2) Chern-Simons theory over $S^4$. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes) and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.