Speaker
Ron Donagi
(UPenn)
Description
Albert Schwarz has made some of the most decisive early contributions to the theory of super Riemann surfaces and its connections with perturbative superstring theory. This subject has been revisited in recent works of Witten, and is rapidly developing in the form of super algebraic geometry. In this talk I will survey some of these recent developments.
We will study various aspects of supergeometry, including obstruction,
Atiyah, and super-Atiyah classes. This will be applied to the geometry of the moduli space of super Riemann surfaces. We prove that for genus greater than or equal to 5, this moduli space is not projected (and in
particular is not split): it cannot be holomorphically projected to its
underlying reduced manifold. Physically, this means that certain
approaches to superstring perturbation theory that are very powerful in
low orders have no close analog in higher orders. Mathematically, it
means that the moduli space of super Riemann surfaces cannot be
constructed in an elementary way starting with the moduli space of
ordinary Riemann surfaces. It has a life of its own. If time allows, we will describe some of the other new features of this space. (This is based on joint with E. Witten)
Primary author
Ron Donagi
(UPenn)
