### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

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

**Path integral bosonization of massive GNO fermions.** / Park, Q Han; Shin, H. J.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 506, no. 1-2, pp. 537-547.

}

TY - JOUR

T1 - Path integral bosonization of massive GNO fermions

AU - Park, Q Han

AU - Shin, H. J.

PY - 1997/11/24

Y1 - 1997/11/24

N2 - 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.

AB - 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.

KW - Bosonization

KW - Conformal field theory

KW - Non-Abelian sine-Gordon theory

KW - Soliton

UR - http://www.scopus.com/inward/record.url?scp=0031585609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031585609&partnerID=8YFLogxK

M3 - Article

VL - 506

SP - 537

EP - 547

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -