Theory of Elementary Particles

该提议是为了研究各种领域理论中的二元性。特别地，我们将在二维西格玛模型中研究目标空间的对偶性。特别强调揭示量子场论中的几何结构。几何方法也将被用来研究2，3和4维1/N展开式中的Yang-Mills理论。该提议的另一个方面是研究有边界的可积量子场论。一个这样的模型是具有较高自旋守恒电荷的Sine-Gordon模型。由于模型的精确可解性，人们希望能深入了解带边界的理论的非微扰方面。这对于膜世界物理以及许多凝聚态系统都具有重要的意义。

The proposal is to study duality in various field theories. In particular target space duality will be investigated in two dimensional sigma models. Particular emphasis will be placed on uncovering geometrical structure in quantum field theories. Geometrical methods will also be used to study Yang-Mills theory in the 1/N expansion in 2, 3 and 4 dimensions.Another aspect of the proposal is to study integrable quantum field theories that have boundaries. One such model is the sine-Gordon model with higher-spin conserved charges. Due to the exact solvability of the model, one hopes to gain insight into the non-perturbative aspects of theories with boundaries. This has important significance for brane-world physics as well as many condensed matter systems.