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Diagrammatic state sums for 2D pin-minus TQFTs

Turzillo, Alex (2020) Diagrammatic state sums for 2D pin-minus TQFTs. Journal of High Energy Physics, 2020 (3). Art. No. 19. ISSN 1029-8479.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Turzillo, Alex0000-0003-4293-4293
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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Subject Keywords:Topological Field Theories, Lattice Quantum Field Theory, Topological States of Matter
Issue or Number:3
Record Number:CaltechAUTHORS:20200304-143651014
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Official Citation:Turzillo, A. Diagrammatic state sums for 2D pin-minus TQFTs. J. High Energ. Phys. 2020, 19 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101713
Deposited By: Tony Diaz
Deposited On:04 Mar 2020 22:42
Last Modified:04 Mar 2020 22:42

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