Integrable field theories in higher dimensions and infinite-dimensional symmetries

我们在以下两个方面进行了研究：一、可积场论在不同方向上的扩展二、统一理论下的场论新模型我们在以下几个问题上取得了一些成果。在本研究的过程中，我们还发现了新的问题：(A)Guttmann-Enting猜想的检验：(B)带边界的可积格子模型及其场论极限(C)含有手征费米子的可积模型和格子上的SuSY模型(D)三维扩展的SuSY NLSM的紫外线发散性质(E)二维可积场论的非对易扩展(F)Wess-Zumino-Witten模型向高维的推广(G)Calogero-Moser模型的量子理论：关于根系和Lax的新结果(H)Calogero-Moser模型的量子理论：具有简并势的模型的可积性。II.(A)作为Higgs场起源的高维规范理论(B)不同维场理论之间的对偶：反对称张量场和非线性Sigma模型之间的对偶。在本项目的三年中，我们发表了19篇论文。

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.