2001 Fiscal Year Final Research Report Summary
Integrable Field Theories in Higher Dimensions and Supersymmetry
| Project/Area Number |
10209209
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Chuo University |
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Principal Investigator |
INAMI Takeo Chuo Univ, Faculty of Science and Engin, Professor, 理工学部, 教授 (20012487)
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| Co-Investigator(Kenkyū-buntansha) |
KANNO Hiroaki Nagoya Univ, Dept of Math Science, Assoc Professor, 大学院・多元数理科学研究科, 助教授 (90211870)
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| Project Period (FY) |
1998 – 2001
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| Keywords | Integrable field theory / Supersymmetry / Higher- dimensional gauge theory / Non-linear sigma model / Non-commutative field theory / Soliton / Instanton / Exceptional holonomy group |
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| Research Abstract |
During the last four years we have carried out research on a few subjects as we palanned originally :
I. Extension of integrable models in various directions
II. New models of field theories, new class of beyond-the-standard models
III. Higher-dimensional gauge theories
IV. M theory and geometry
We have obtained results on a few problems concerning these subjects.
I. (a) Test of the Guttmann-Enting conjecture on solvability of low- dimensional models
(b) Continuum limit of lattice models with a boundary : XYZ spin 1/2 chain and the sine-Gordon theory
(c) Integrable models containing chiral fermions and SUSY on the lattice in d = 2
(d) Ultraviolet divergence properties of the extended (N = 2, 4) SUSY NLSM in d = 3
II. (a) i) Non-commutative extension of the Wess-Zumino-Witten model, ii) Low -energy dynamics of solitons in the non-commutative CP(n) model in d = 3
(b) Duality between field theories in diverse dimensions
(c) The 3-3-1 gauge model in view of higher-dimensional gauge theories
III. (a) Higher-dimensional gauge theories as the origin of the Higgs field
(b) Higher-dimensional SUSY gauge theories : Moduli space of the instanton equation and geometry of supsersymmetric cycles
c Five-dimensional SUSY gauge theories : Mirror symmetry and the instanton expansion of the prepotential
IV. (a) Geometry of manifolds with exceptional holonomy group : the metric of the manifolds with G_2 and Spin(7) holonomy groups, and gravitational instantons in higher dimensions
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