Bicategorical String Nets in Quantum Symmetries

Explore the intricacies of bicategorical string nets in this one-hour lecture by Jürgen Fuchs at the Centre de recherches mathématiques (CRM). Delve into the string-net construction using colored graphs embedded in surfaces to produce a modular functor. Learn why pivotal bicategories are the appropriate algebraic input for coloring, rather than spherical fusion categories. Examine the relationships between different string-net constructions through Frobenius functors. Investigate specific bicategories of interest, including Fr(C) of Frobenius algebras in modular fusion categories and the delooping BC. Discover how this framework enables a two-dimensional construction of consistent correlator systems for rational CFTs. Understand the role of Fr(C)-colored string nets in capturing local rules for defects in world sheets with the same correlator. Gain insights into how these concepts fit into the framework of double categories, alongside field functors in CFT applications.

Jürgen Fuchs: Bicategorical string nets