A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories

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发表日期：

2025年9月1日

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Cameron Krulewski,
Luuk Stehouwer,
Lukas Müller

摘要

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