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SUMMARY:Yang Yang: RCFT correlators as equivalences of modular functors
DTSTART:20240521T083000Z
DTEND:20240521T093000Z
DTSTAMP:20240622T134900Z
UID:indico-event-12033@indico.math.cnrs.fr
DESCRIPTION:The local information of a 2d rational conformal field theory
(RCFT) is encoded in a vertex operator algebra\, whose modules constitute
a modular fusion category C. The collection of global observables of the t
heory is given by conformal blocks and carries actions of mapping class gr
oups\, which is described mathematically by a modular functor that assigns
the Drinfeld center Z(C) to a circle. The string-net construction\, first
appeared in the study of topological phases of matter\, not only provides
such a modular functor but also supplies a graphical construction of corr
elators. A generalization of the string-net construction takes a pivotal b
icategory as input. When such a bicategory is taken to be C (considered as
a bicategory)\, it recovers the modular functor of conformal blocks. On t
he other hand\, the modular functor associated with the Morita bicategory
of separable symmetric Frobenius algebras internal to C classifies stratif
ied worldsheets up to "categorical symmetries". In this talk we explain\,
using the framework of double categories\, that RCFT correlators exhibit a
n equivalence between these modular functors. More generally\, the modular
functors associated with a pivotal bicategory and its orbifold completion
are canonically equivalent.\n\nhttps://indico.math.cnrs.fr/event/12033/
LOCATION:Salle 318 (IMB)
URL:https://indico.math.cnrs.fr/event/12033/
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