Integrable Field Theories in Higher Dimensions and Supersymmetry

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

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