Integrable field theories in higher dimensions and infinite-dimensional symmetries

我们对以下两个问题进行了研究：I.可积场论的各种方向的推广II.统一理论观点下的场论新模型我们对以下问题取得了一些结果。在研究过程中，我们也发现了一些新的问题。(a)古特曼-恩廷猜想的检验：八顶点模型（B）具有边界的可积晶格模型及其场论极限（c）晶格上包含手征费米子和超对称模型的可积模型（d）三维中扩展超对称非线性最小二乘模型的紫外发散性质（e）二维可积场论的非对易扩展（f）Wess-Zumino-维滕模型向高维的扩展（g）Calogero-Moser模型的量子理论：关于根系和Lax表示的新结果。(h)Calogero-Moser模型的量子理论：退化势模型的可积性. II. (a)作为希格斯场起源的高维规范理论（B）不同维度场论之间的对偶性：反对称张量场与非线性sigma模型之间的对偶性。

We have carried out research on the following two subjects :I.Extension of integrable field theories in various directionsII.New models of field theories in view of unified theoriesWe have obtained a few results on the following problems. We have also found new problems in the course of the present research.I.(a) Test of Guttmann-Enting's conjecture : eight-vertex model(b) Integrable lattice models with boundaries and their field theory limit(c) Integrable models containing chiral fermions and SUSY models on the lattice(d) Ultraviolet divergence properties of the extended SUSY NLSM in three dimensions(e) Non-commutative extension of two-dimensional integrable field theories(f) Extension of the Wess-Zumino-Witten model to higher dimensions(g) Quantum theory of Calogero-Moser model : New results on root systems and Lax representation.(h) Quantum theory of Calogero-Moser model : Integrability of models with degenerate potential.II.(a) Higher dimensional gauge theories as the origin of Higgs fields(b) Duality between field theories in diverse dimensions : Duality between antisymmetric tensor fields and nonlinear sigma models.We have published 19 papers during the three years of this project term.