Turaev-Viro-Barrett-Westbury invariants with defects

Abstract: Turaev-Viro-Barrett-Westbury state sum models are concrete constructions of TQFTs based on triangulated 3-manifolds and spherical fusion categories. Introducing defects in these models is of interest for defect TQFTs and for applications in condensed matter physics.

In the talk we explain how to construct Turaev-Viro-Barrett-Westbury state sums with defects in terms of generalised 6j symbols. Defect surfaces are labeled with bimodule categories over spherical fusion categories, defect lines and points form graphs on these surfaces and are labeled with bimodule functors and bimodule natural transformations. We show that the resulting state sums are triangulation independent, compute examples and interpret them.

Based on arxiv.org/abs/2205.06874

Mathematics

Audience: researchers in the topic

( paper )

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European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home

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