Lecturer: Prof. Ron Donagi
Affiliation: Department of Mathematics,
University of Pennsylvania
Abstract:
Super Riemann surfaces exhibit
many of the familiar features of
ordinary Riemann surfaces, and
some novelties. They have
moduli spaces and Deligne-
Mumford compactifications.
One can integrate and construct
measures on moduli spaces. The
punctures one can insert come
in two varieties: Ramond and
Neveu-Schwarz.
I will survey some of the
expected and unexpected
features, emphasizing a recent
proof that for genus g \geq 5,
the moduli space of super
Riemann surfaces 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.
When we examine the Deligne-
Mumford compactification of
moduli space, and especially the
Ramond boundary divisors, we
find that the interesting new
phenomena start already at one
loop. This is interpreted as the
mechanism that allows
supersymmetry to remain
unbroken at tree level in certain
models of superstring
perturbation theory, but to be
spontaneously broken at one
loop.
(This is joint work with E.
Witten)
Additional details of the upcoming High Energys'
seminars can be found on the following link.