A Chern-Simons effective field theory for the Pfaffian quantum Hall state

Eduardo Fradkin, Chetan Nayak, Alexei Tsvelik, Frank Wilczek

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We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.

Original languageEnglish (US)
Pages (from-to)704-718
Number of pages15
JournalNuclear Physics B
Issue number3
StatePublished - Apr 20 1998


ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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