Effective field theory description of the higher dimensional quantum Hall liquid

摘要

We derive an effective topological field theory model of the four dimensionalquantum Hall liquid state recently constructed by Zhang and Hu. Using ageneralization of the flux attachment transformation, the effective fieldtheory can be formulated as a U(1) Chern-Simons theory over the totalconfiguration space $CP_3$, or as a SU(2) Chern-Simons theory over $S^4$. Thenew 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 generalizesthe concept of fractional statistics.