Abstract
The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita invariance of the construction are discussed.
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Turzillo, A. Diagrammatic state sums for 2D pin-minus TQFTs. J. High Energ. Phys. 2020, 19 (2020). https://doi.org/10.1007/JHEP03(2020)019
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DOI: https://doi.org/10.1007/JHEP03(2020)019