State sum construction of two-dimensional topological quantum field theories on spin surfaces

DOI10.1142/S0218216515500285zbMath1320.57035arXiv1402.2839OpenAlexW2963766793MaRDI QIDQ5262987

Ingo Runkel, Sebastian Novak

Publication date: 10 July 2015

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2839

zbMATH Keywords

topological field theoryFrobenius algebradefect linescombinatorial spin structurespin surface

Mathematics Subject Classification ID

Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56) Spin and Spin({}^c) geometry (53C27) General geometric structures on low-dimensional manifolds (57M50)

Related Items (12)

Topological field theories on open-closed \(r\)-spin surfaces ⋮ The super Frobenius-Schur indicator and finite group gauge theories on \(\mathrm{pin}^-\) surfaces ⋮ Fermionization of fusion category symmetries in 1+1 dimensions ⋮ Diagrammatic state sums for 2D pin-minus TQFTs ⋮ Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions ⋮ Fully extended \(r\)-spin TQFTs ⋮ String-net models for nonspherical pivotal fusion categories ⋮ Defects in the tri-critical Ising model ⋮ Spin from defects in two-dimensional quantum field theory ⋮ Topological field theory on r-spin surfaces and the Arf-invariant ⋮ Two-dimensional state sum models and spin structures ⋮ Spin TQFTs and fermionic phases of matter

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