Integrable Field Theories in Higher Dimensions and Supersymmetry

高维和超对称中的可积场论

• 批准号: 10209209
• 负责人: INAMI Takeo
• 金额: $ 3.84万
• 依托单位: Chuo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10209209/
• 关键词: Integrable field theory; Supersymmetry; Higher- dimensional gauge theory; Non-linear sigma model; Non-commutative field theory; Soliton; Instanton; Exceptional holonomy group; 可積分支場の理論; 高次元ヤング・ミルズ理論; 可積分な場の理論; 可解模型; 8頂点模型; 双対性; 位相的な場の理論

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 directionsII. New models of field theories, new class of beyond-the-standard modelsIII. Higher-dimensional gauge theoriesIV. M theory and geometryWe 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 = 3II. (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 theoriesIII. (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 cyclesc Five-dimensional SUSY gauge theories : Mirror symmetry and the instanton expansion of the prepotentialIV. (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

在过去的四年里，我们按照我们最初的安排，对几个课题进行了研究：一、可积模型在不同方向上的推广场论的新模型，新的超标准模型。高维规范理论IV。M理论和几何我们已经得到了与这些主题有关的几个问题的结果：(A)关于低维模型可解性的Guttmann-Enting猜想的检验(B)具有边界的格子模型的连续极限：XYZ自旋1/2链和Sine-Gordon理论(C)在d=2的格子上含有手征费米子和Sine-Gordon理论的可积模型(D)扩展的(N=2，4)超SY NLSM在d=3II中的紫外线发散性质。(A)Wess-Zumino-Witten模型的非对易推广；(Ii)d=3的非对易CP(N)模型中孤子的低能动力学；(B)不同维场论之间的对偶性；(C)高维规范理论下的3-3-1规范模型。(A)作为希格斯场起源的高维规范理论；(B)高维超对称规范理论：瞬子方程的模空间和超对称循环的几何；五维超对称规范理论：镜像对称性和预势的瞬子展开。(A)具有例外完整群的流形的几何：具有G_2和自旋(7)完整群和高维引力瞬子的流形的度规

项目成果

H. Kanno: "A Note on Higher-Dimensional Instantons and Supersymmetric Cycles"Prog Theor. Phys.. 135. 18-28 (1999)

H. Kanno：“关于高维瞬时子和超对称循环的注释”Prog Theor。

H.Kanno: "Picard-Fuchs Eguation and Prepatential Five-Dimensional SUSY Gauge Theory Compactified an a Cirde" Nucl.Phys.B530巻. 73-98 (1998)

H. Kanno：“Picard-Fuchs Egation 和 Prepatential 五维 SUSY 规范理论的紧凑化”Nucl.Phys.B530 Vol. 73-98 (1998)

H. Tsukahara, T. Inami: "The Continuum Limit of the Integrable Open Spin-1/2 Chain"J. Phys. Soc. Japan. 68. 319-321 (1999)

H. Tsukahara，T. Inami：“可积开自旋 1/2 链的连续极限”J。

T. Inami, Y. Saito, M. Yamamoto: "Vanishing Next-to-Leading Order Corrections to the Beta Function of the SUSY CP^<N-1> Model in Three Dimensions"Prog. Theor. Phys. 103. 1283-1288 (2000)

T. Inami、Y. Saito、M. Yamamoto：“三维 SUSY CP^<N-1> 模型 Beta 函数的消失次前导阶修正”Prog。

K.Furuto,T.Inami: "Ultraviolet properties of Noncommutative West-Zumino-Witten Model"Mod.Phys.Letters. A15. 997-1002 (2000)

K.Furuto，T.Inami：“非交换 West-Zumino-Witten 模型的紫外特性”Mod.Phys.Letters。