String-net models, conformal field theories with defects and double categories

18.05.2022 14:15 - 15:15

Yang Yang (U Hamburg)

Abstract: In this talk, I will present a generalized version of string-net models that have pivotal bicategories as input data and showcase their application to 2-dimensional (rational) conformal field theories.

When the input datum is chosen to be a modular fusion category C viewed as a single-object pivotal bicategory, the construction recovers the string-net model formalized by Kirillov Jr. as a 2-dimensional skein theory and provides an open-closed modular functor that assigns the Drinfeld center Z(C) to a circle, which serves as an concrete model for the spaces of conformal blocks for an RCFT with fixed chiral data.

On the other hand, if we choose the bicategory to be that of frobenius algebras, bimodules and bimodule morphisms internal to C, we get a modular functor that classifies the worldsheets with defects for the said RCFT, where the equivalence relation on the worldsheets is generated by the local graphical calculus of the defects.

The crucial observation is that the two modular functors provided by the string-net construction extend to two symmetric monoidal double functors between double categories of bordisms and profunctors, and that the a consistent system of correlators for all worldsheets corresponds to a monoidal vertical transformation between the double functors.

The talk is based on joint work 
with Jürgen Fuchs (Karlstad) and Christoph Schweigert (Hamburg).
Meeting ID: 642 6819 0404, Passcode: 968132

N. Schuch
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