Higher-Dimensional Quantum Hall Effect in String Theory

TL;DR

This paper models the 4+1 dimensional quantum Hall effect within string theory, using D-branes and instantons, and explores a hierarchy of such effects in odd-dimensional spacetimes.

Contribution

It provides a string theory construction of higher-dimensional quantum Hall effects and introduces a hierarchy extending to odd dimensions.

Findings

Realization of 4+1d quantum Hall effect via D-branes and instantons

Large n limit configuration space approaches CP^3

Hierarchy of quantum Hall effects in odd-dimensional spacetimes

Abstract

We construct a string theory realization of the 4+1d quantum Hall effect recently discovered by Zhang and Hu. The string theory picture contains coincident D4-branes forming an S^4 and having D0-branes (i.e. instantons) in their world-volume. The charged particles are modelled as string ends. Their configuration space approaches in the large n limit a CP^3, which is an S^2 fibration over S^4, the extra S^2 being made out of the Chan-Paton degrees of freedom. An alternative matrix theory description involves the fuzzy four-sphere. We also find that there is a hierarchy of quantum Hall effects in odd-dimensional spacetimes, generalizing the known cases in 2+1d and 4+1d.