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Diagrammatic State Sums for 2D Pin-Minus TQFTs

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.

preprint2020arXivOpen access
Alex Turzillo
cond-mat.str-elmath.QAhep-th
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Alex Turzillo

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