Twisted modules over vertex algebras have many applications in
mathematical physics. In particular, twisted modules over the
vertex algebra associated to an untwisted affine Kac-Moody algebra are
nothing but representations of the corresponding twisted affine Lie
algebra. In this talk, based on a joint work with Matthew
Szczesny, I will explain how to interpret the twisted module
structure geometrically, as a section of a certain flat vector bundle
on the covering of a formal disc. This interpretation allows us
to define the space of conformal blocks associated to a curve
together with a covering and twisted modules attached to all ramification
points. These spaces should combine into sheaves on various
moduli spaces such as Hurwitz schemes. They are the building blocks
of the corresponding orbifold conformal field theory.
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