Bound States, Singularities, and Supersymmetry

Duke University, Durham NC

Investigators

Abstract

ABSTRACT DMS - 0204188. The principal investigator will seek analytic realizations of "stringy" cohomology of singular varieties with trivial canonical bundle. He will study the implications of such analytic realizations (and their generalizations) towards providing new explanations of gauge symmetry enhancement mechanisms in string theory. In collaboration with S. Sethi, the PI will continue his program to 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 L2 kernels give the ground states for this theory. Sethi and the PI will examine methods for computing gravitational anomalies of field theories arising from string theories on singular spaces. S. Paban, S. Sethi, and the PI will examine the constraints imposed by supersymmetry on deformations of the supersymmetry algebra associated to an isolated five brane. The PI will investigate the extension 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 which incorporates 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 a mathematical model for the physical interactions between certain "particles" known as 5 branes, whose existence is predicted by M theory.