Moduli Spaces and String Theory

Duke University, Durham NC

Investigators

Abstract

This proposal will analyze the structure of moduli spaces, i.e., versions of parameter spaces, in the context of superstrings propagating on Calabi-Yau manifolds. Three moduli spaces will be considered: the space of N=(2,2) superconformal field theories, which relates directly to the moduli space of the Calabi Yau threefolds; the space of N=(0,2) superconformal field theories, which extends this notion to something closer to real physics and is associated with the moduli spaces of vector bundles; and D-branes on a fixed Calabi Yau manifold which is associated to the moduli space of stable objects in the derived category. Superstring theory is a model of fundamental physics expected to yield a unified description of fundamental particle physics and the structure of spacetime. While this theory has yet to make contact with experimental physics, its impact and success in field of mathematics in areas such as algebraic geometry is beyond doubt. The proposed research intends to both build on established links between methods of theoretical physics and geometry, and pursue as yet unexplored connections. The main notion explored in this proposal is the idea of a set of all possible mathematically consistent theories. This notion can be pursued in the language of either theoretical physics or mathematics. Comparisons between these languages then often yields new ideas and results.