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 CP3, or as a SU(2) Chern-Simons theory over S4. The new quantum Hall liquid supports various types of topological excitations, including the o-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.
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy