TY - JOUR

T1 - Path integral bosonization of massive GNO fermions

AU - Park, Q. Han

AU - Shin, H. J.

N1 - Funding Information:
This work was supported in part by the program of Basic Science Research, Ministry of Education BSRI-96-2442, and by Korea Science and Engineering Foundation through CTP/SNU.

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

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U2 - 10.1016/S0550-3213(97)00539-7

DO - 10.1016/S0550-3213(97)00539-7

M3 - Article

AN - SCOPUS:0031585609

VL - 506

SP - 537

EP - 547

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -