A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories
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Author(s)
Krulewski, Cameron
Stehouwer, Luuk
Müller, Lukas
Date Issued
September 1, 2025
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Krulewski, C., Stehouwer, L. & Müller, L. A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories. Commun. Math. Phys. 406, 230 (2025).
Version
Author's final manuscript
Abstract
We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin statistics theorem. To formulate this extension, we define a higher spin action of the stable orthogonal group O on appropriate spacetime manifolds, which extends both the reflection involution and spin flip. On the algebraic side, we define a higher statistics action of O on the universal target for invertible field theories, I Z , which extends both complex conjugation and fermion parity ( - 1 ) F . We prove that every unitary invertible quantum field theory intertwines these actions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-025-05405-3
