Title:Categorical aspects of conformal field theory
Abstract:
Many aspects of two-dimensional conformal field theory (CFT) can
be formulated and analyzed in terms of the representation category
of the vertex algebra that encodes the symmetries of the theory.
In particular, for rational CFT, for which the category has the
structure of a modular tensor category, the category together with
a certain Frobenius algebra object provides sufficient information
for constructing all correlation functions.
I will describe the main ingredients of this construction and some
of the relevant mathematical tools. Afterwards I discuss how some
of the structures present in rational CFT may generalize to the
non-rational case.