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Quantum Topology

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Volume 10, Issue 3, 2019, pp. 399–439
DOI: 10.4171/QT/121

Published online: 2018-10-31

Line and surface defects in Reshetikhin–Turaev TQFT

Nils Carqueville[1], Ingo Runkel and Gregor Schaumann[2]

(1) Universität Wien, Austria
(2) Universität Wien, Austria

A modular tensor category $\mathcal C$ gives rise to a Reshetikhin–Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal C$-coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. The surface defects are labelled by $\Delta$-separable symmetric Frobenius algebras and the line defects by “multi-modules” which are equivariant with respect to a cyclic group action. Our invariant cannot distinguish non-isotopic embeddings of 2-spheres, but we give an example where it distinguishes non-isotopic embeddings of 2-tori.

Keywords: Topological quantum field theory, Reshetikhin–Turaev theory, orbifolds, stratified bordisms

Carqueville Nils, Runkel Ingo, Schaumann Gregor: Line and surface defects in Reshetikhin–Turaev TQFT. Quantum Topol. 10 (2019), 399-439. doi: 10.4171/QT/121