Path integral bosonization of massive GNO fermions

Q. Han Park, H. J. Shin

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces K/G. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable g takes value in the orthogonal, unitary, and symplectic representations of the group G in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces K/G are SU(N) × SU(N)/SU(N); N ≤ 3, Sp(2)/U(2) or SO(8)/U(4). We also address the relation between massive GNO fermions and the non-Abelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.

Original languageEnglish
Pages (from-to)537-547
Number of pages11
JournalNuclear Physics B
Issue number1-2
Publication statusPublished - 1997 Nov 24
Externally publishedYes


  • Bosonization
  • Conformal field theory
  • Non-Abelian sine-Gordon theory
  • Soliton

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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