Mathematical Sciences/GIG: A Team Approach to String Theory

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This activity is intended to foster the interdisciplinary collaboration between the research groups headed by Shing-Tung Yau in the Harvard Mathematics Department and Cumrun Vafa in the Harvard Physics Department. Vafa's group has furthered our understanding of the non-perturbative aspects of string theory along several fronts: deriving the Seiberg-Witten results as a low-energy limit of the moduli dependence of the prepotential in string theory; studying D-brane physics and relating the counting of BPS states to topological questions, including instantons on K3; geometrizing the SL(2,Z) invariance of the Type IIB string and postulating a twelve-dimensional theory (``F-theory"), which contains many interesting string dualities; developing a geometric understanding of non-abelian gauge symmetries and confinement in string theory; and describing the Beckenstein-Hawking entropy of black holes in terms of counting states via string theory and string duality. This last result is perhaps the most striking revelation in quantum gravity from string theory. Yau's group has been instrumental in understanding several aspects of mirror symmetry and string dualities: interpreting BPS state counting in terms of enumerative geometry; investigating the differential equations of period integrals on Calabi-Yau manifolds; solving the large radius limit problem in general, which is crucial for applying mirror symmetry to enumerative geometry; describing mirror manifolds as the moduli spaces of supersymmetric submanifolds; and classifying K3 fibrations, which are the key to heterotic-Type II duality. This GIG Award will sponsor postdoctoral research fellows and visiting scholars in mathematics and string theory (physics). String theory has undergone a revolution during the past year but will languish without fresh mathematical results --- for the many conjectures need to be justified with rigor! The pace of mathematics needs to quicken in order to accommodate this recent influx of remarkable ideas. T his is a very exciting time for mathematics, as well. Hard conjectures abound, with physical reasoning providing guidance for serious investigation. Likewise, the physics of string theory is hungry for new math. Within these two groups there is a wealth of intellectual resources. Mathematics and physics will both greatly benefit from full exploitation of this interdisciplinary collaboration.