Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

✍ Scribed by Bogdan Andrei Bernevig; Chyh-Hong Chern; Jiang-Ping Hu; Nicolaos Toumbas; Shou-Cheng Zhang

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 189 KB
• Volume: 300
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2002.6292

✦ Synopsis

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 C P 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.