Focused Research Group: Calabi-Yau Manifolds and their Applications

Abstract

Award: DMS-0074177

Principal Investigator: Michael R. Douglas

This research project brings together a team of mathematicians

and physicists based at three campuses to work together on string

theory. Specific research tasks include the study of the quantum

corrections to the mypermultiplet moduli spaces in theories with

eight supercharges, the structure of the moduli spaces of

heterotic string compactifications, M-theory models compactified

on seven-dimensional spaces whose global holonomy group lies in

the exceptional Lie group G2, M-theory models on Calabi-Yau

fourfolds, and a study of the AdS/CFT correspondence for branes

at singularities.

String theory is a promising candidate for a unifying theory of

the universe at its most fundamental levels. Although the basic

idea is simple - elementary particles should be modeled as

mathematical loops of stgring rather than as points - working out

the details of this theory has involved and inspired some

sophisticated mathematical tools and ideas. The task is by no

means complete, even in an area where the synergy between

mathematics and physics has been particularly productive, the

study of the Calabi-Yau spaces that appear as solutions of the

classical string equations of motion. This is one of three

linked awards to a research group that includes mathematicians

and physicists at Duke University, Columbia University, and

Rutgers University, and NSF funds are supporting this

interdisciplinary group's collaborations through

videoconferencing and travel.