Theory of Elementary Particles

建议在各种场论中研究对偶性。特别是目标空间的对偶性将在二维sigma模型中进行研究。特别的重点将放在揭示几何结构在量子场论。几何方法也将被用于研究杨-米尔斯理论在2、3和4维的1/N展开。该提议的另一个方面是研究具有边界的可积量子场论。其中一个模型是具有更高自旋守恒电荷的正弦戈登模型。由于模型的精确可解性，人们希望深入了解具有边界的理论的非摄动方面。这对膜世界物理以及许多凝聚态体系都具有重要意义。

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.