High Energy Theory Seminar
5 April 2011
Michael Schulz (Bryn Mawr College & MIT)
T-folds, Doubled Geometry, and
the SU(2) WZW Model
Abstract:
Generalized compactifications of string theory relax the condition that
there be a globally well defined space in the extra dimensions. We give
up the usual distinction between a Riemannian manifold and other fields
living on that manifold, so that the two become intrinsically
intertwined. Such compactifications are the natural result of lifting
generic gauging of lower dimensional supergravity theories to the full
10D string theory.
But, what is the topological choice that *defines* such a string theory
compactification? In my talk, I will advocate one possible
answer: the "doubled geometry" seen simultaneously by left plus right
moving string excitations. This geometry neatly packages the
fields into purely metric degrees of freedom. Its topology
unifies the traditional choice of spatial topology and magnetic flux
into a single generalized choice. I'll begin with a simple motivating
example, then describe the framework of Hull and Reid-Edwards for
locally reconstructing physical from doubled geometry. Finally,
I'll describe insights from applying this framework to the SU(2) WZW
model, a simple soluble model which nevertheless exhibits interesting
and surprising features.
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