Effective field theory description of the higher dimensional quantum hall liquid

Bogdan Andrei Bernevig, Chyh Hong Chern, Jiang Ping Hu, Nicolaos Toumbas, Shou Cheng Zhang

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)185-207
Number of pages23
JournalAnnals of Physics
Issue number2
StatePublished - Sep 15 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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