Application of methods of arithmetic geometry and homological algebra to quantum field theory and string theory

University Of California-Davis, Davis CA

Investigators

Abstract

Abstract Award: DMS-0805989 Principal Investigator: Albert Schwarz The first of these projects concerns applications of p-adic methods to topological strings. The goal of these projects is to express physical quantities in terms of arithmetic geometry over p-adic numbers and to use these expressions to prove integrality theorems. Another set of investigations deals with supersymmetric deformations of quantum field theories. This is joint work with M. Movshev and applies the theory of L-infinity and A-infinity algebras. Another project is devoted to the analysis of the relation between string theory and quantum field theory. The principal investigator has argued that quantum field theory can be formulated such that time and space do not appear as primary notions, and is planning to show that string theory can be regarded as a quantum field theory in this sense. These research projects are based on the application of methods of modern mathematics to physics, particularly making use of arithmetic geometry and homological algebra to improve our understanding of quantum field theory and string theory. Sophisticated mathematics originally developed for other purposes such as the study of Diophantine equations in number theory seems to bear directly on challenging issues in theoretical physics.