### Abstract

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 language | English |
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Pages (from-to) | 537-547 |

Number of pages | 11 |

Journal | Nuclear Physics B |

Volume | 506 |

Issue number | 1-2 |

Publication status | Published - 1997 Nov 24 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*506*(1-2), 537-547.