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 |
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Keywords
- Bosonization
- Conformal field theory
- Non-Abelian sine-Gordon theory
- Soliton
ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
Path integral bosonization of massive GNO fermions. / Park, Q Han; Shin, H. J.
In: Nuclear Physics B, Vol. 506, No. 1-2, 24.11.1997, p. 537-547.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:0031585609
VL - 506
SP - 537
EP - 547
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 1-2
ER -