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arXiv · 2301.06664

Reflection Structures and Spin Statistics in Low Dimensions

Lukas Müller·Luuk Stehouwer
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Abstract

We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group $G$ which is different from the spacetime structure group. Fermionic groups encode symmetries of systems with fermions and time reversing symmetries. We show that 1-dimensional topological field theories with reflection structure and spin-statistics are classified by finite dimensional hermitian representations of $G$. In spacetime dimension two we give a classification in terms strongly $G$-graded stellar Frobenius algebras. Our proofs are based on the cobordism hypothesis. Along the way, we develop some useful tools for the computation of homotopy fixed points of 2-group actions on bicategories.

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Lukas Müller, Luuk Stehouwer. 2023-01-17. Reflection Structures and Spin Statistics in Low Dimensions. https://doi.org/10.1142/s0129055x24500351

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