Domain Walls Between 3d Phases of Reshetikhin–Turaev TQFTs

We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin–Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we present an explicit and computable construction of such defects. I...

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Bibliographic Details
Published in:Communications in mathematical physics 2022-12, Vol.396 (3), p.1187-1220
Main Authors: Koppen, Vincent, Mulevičius, Vincentas, Runkel, Ingo, Schweigert, Christoph
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Domain walls
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Quantum theory
Relativity Theory
Surface defects
Theoretical
Topology
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Summary:We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin–Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we present an explicit and computable construction of such defects. It specialises to the construction in Carqueville et al. (Geom Topol 23:781–864, 2019. https://doi.org/10.2140/gt.2019.23.781 . arXiv:1705.06085 ) if all 3-strata are labelled by the same topological field theory. We compare the results to the model-independent analysis in Fuchs et al. (Commun Math Phys 321:543–575, 2013. https://doi.org/10.1007/s00220-013-1723-0 . arXiv:1203.4568 ) and find agreement.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04489-5