Higher-Dimensional Quantum Hall Effect in String Theory

الأصل · EN

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 S⁴ 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 CP³, which is an S² fibration over S⁴, the extra S² 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.