Bound States, Singularities, and Supersymmetry

摘要DMS -0204188.主要研究者将寻求具有平凡标准丛的奇异簇的“弦“上同调的解析实现。他将研究这种分析实现（及其推广）的含义，以提供弦理论中规范对称性增强机制的新解释。与S合作。塞西，PI将继续他的计划，以分析超对称矩阵模型量子力学，这已被证明是提供一个定义的M理论。研究生G.凡士通，将研究非Fredholm狄拉克算子的L2指数理论，其L2核给出了该理论的基态。塞西和PI将检查方法计算引力异常的场论所产生的弦理论在奇异空间。S. Paban，S. Sethi和PI将检查超对称性对与孤立的五膜相关的超代数变形的约束。PI将研究扩展维滕的旋量技术证明的正质量猜想通过取代假设的自旋结构退化的一个光滑的自旋结构上的一个余维2子流形。M理论提供了一个潜在的框架，提供一个物理理论，它结合了引力和描述高能粒子的量子物理。这一理论的确切形式尚未完全发展。可衡量的后果甚至还远未完全确定。这个项目试图确定，对于这个理论的分支，基本的后果，如不同类型的粒子的数量，当这些粒子联合收割机组合成更复杂的物质时，以及这些粒子及其组合的大小和形状。除了发展M和弦理论的物理后果，这样的计算可以用来检查M理论的基本假设中的潜在错误。该项目还寻求更好地理解某些称为5膜的“粒子”之间物理相互作用的数学模型，其存在由M理论预测。

ABSTRACT DMS - 0204188.The principal investigator will seek analytic realizations of "stringy"cohomology of singular varieties with trivial canonical bundle. He will studythe implications of such analytic realizations (and their generalizations)towards providing new explanations of gauge symmetry enhancement mechanisms instring theory. In collaboration with S. Sethi, the PI will continue his programto analyze the supersymmetric matrix model quantum mechanics which has been conjectured to provide a definition of M theory. Graduate student G. Firestone, will study the L2 index theory for the nonFredholm Dirac operators whose L2kernels give the ground states for this theory. Sethi and the PI will examinemethods for computing gravitational anomalies of field theories arising fromstring theories on singular spaces. S. Paban, S. Sethi, and the PI will examinethe constraints imposed by supersymmetry on deformations of the supersymmetryalgebra associated to an isolated five brane. The PI will investigate theextension of Witten's spinor technique of proving the positive mass conjecture by replacing the hypothesis of a smooth spin structure by the assumption of a spin structure degenerating on a codimension 2 submanifold.M theory gives a potential framework for providing a physical theory whichincorporates both gravitation and the quantum physics describing high energy particles. The precise form of this theory is not yet fully developed. The measurable consequences are even further from being fully worked out. This project attempts to determine, for branches of this theory, fundamental consequences, such as the number of particles of different types, when these particles combine to make more complex matter, and the size and shape of these particles and their combinations.In addition to developing the physical consequences of M and string theory,such computations can be used to check for potential errors in the underlying hypotheses of M theory. This project also seeks a better understanding of amathematical model for the physical interactions between certain "particles" known as 5 branes, whose existence is predicted by M theory.