AG Mathematische Physik, Dr. Simon Wood (Cardiff, Hamburg): Lie theory beyond category O in conformal field theory and vertex,operator algebras

Dr. Simon Wood

Lie theory beyond category O in conformal field theory and vertex
operator algebras

Abstract:
Affine Lie algebras provide the means for constructing some of the best
understood conformal field theories or vertex operator algebras. If the
level of the affine Lie algebra is non-negative integral, then the
integrable modules form a modular tensor category (among many other
properties, this implies an action of the modular group on characters).
In this talk I will give an overview of why this is highly desirable
from the perspective of conformal field theory and some new results on
modular properties and their consequences at certain non-integral
levels, called admissible levels. No prior knowledge of vertex operator
algebras or conformal field theory will be assumed. I will do my best to
motivate everything through Lie theory.