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arXiv · 2408.03981

A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories

Cameron Krulewski·Lukas Müller·Luuk Stehouwer
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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, $I\mathbb{Z}$, which extends both complex conjugation and fermion parity $(-1)^F$. We prove that every unitary invertible quantum field theory intertwines these actions.

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Cameron Krulewski, Lukas Müller, Luuk Stehouwer. 2024-08-07. A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories. https://doi.org/10.1007/s00220-025-05405-3

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