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Published March 2020 | Submitted + Published
Journal Article Open

Diagrammatic state sums for 2D pin-minus TQFTs

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.

Additional Information

© 2020 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: September 8, 2019; Accepted: February 18, 2020; Published: March 3, 2020. Article funded by SCOAP3. The author is especially grateful to John Barrett for acquainting me with the key references [7, 15], for productive discussions in the early stages of this project, and for sharing his thoughts on the manuscript. I would also like to thank Dave Aasen, Matt Heydeman, Nick Hunter-Jones, Anton Kapustin, and Eric Samperton for enlightening conversations and Arun Debray for valuable commentary on the manuscript. This work was performed partly at Fudan University and was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632 as well as the Simons Investigator Award.

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Published - Turzillo2020_Article_DiagrammaticStateSumsFor2DPin-.pdf

Submitted - 1811.12654.pdf

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Created:
August 19, 2023
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October 19, 2023