4th Seminar on Conformal Field Theory
June 26th, 2015
Technische Universität Darmstadt
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Abstracts of the talks
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Catherine Meusburger: Hopf algebra gauge theory from Kitaev lattice
models
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Kitaev lattice models play an important role in topological quantum
computing and are closely related to 3d TQFTs of Reshetikhin-Turaev and
of Turaev-Viro type. We show how a Kitaev model based on a
finite-dimensional, semisimple Hopf algebra H gives rise to a Hopf
algebra lattice gauge theory for the Drinfeld double D(H). This relates
Kitaev models to known combinatorial quantisation formalisms for
Chern-Simons gauge theory. On the other hand it allows one to construct
Poisson-geometrical counterparts of these models, which can be viewed as
a classical limit and describe the symplectic structure on moduli spaces
of flat connections.
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Sven Möller: Simple Currents, AIAs and Orbifold Construction of
Holomorphic VOAs
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"Nice" (= rational, C_2-cofinite, simple, self-contragredient, of
CFT-type) VOAs whose irreducible modules are all simple currents have a
very beautiful representation theory. Moreover, the sum of all these
modules admits the structure of an abelian intertwining algebra (AIA).
We will study the case of a "nice" holomorphic VOA V and the fixed-point
subVOA V^g for some automorphism of V of order n. V^g is also "nice" and
its n^2 irreducible modules are all simple currents. We can show that
the direct sum Ṽ of certain n of these V^g-modules carries a VOA
structure. This proves the orbifold construction for an arbitrary finite
cyclic group of automorphisms.
As an application we construct 5 new cases on Schellekens' list of 71
"nice" holomorphic VOAs of central charge 24.
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Christoph Schweigert: Representations of mapping class groups and
invariants from finite ribbon categories
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We explain how finite ribbon categories give rise to representations of
mapping class groups of Riemann surfaces and how to construct invariants
of this action from commutative Frobenius algebras. Semisimplicity is
not required in these constructions.