From the 1 of 10 linked papers with an AI index.
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Weak topological phases in the presence of interactions
Omar AntolÃn Camarena, Arun Debray, Cameron Krulewski +3
The paper classifies weak symmetry‑protected topological phases in dimensions 0–3 under short‑range interactions, using homotopy‑theoretic methods to identify which phases remain s…
Unraveling the Bott spiral
Arun Debray, Cameron Krulewski, Luuk Stehouwer
We construct and compute a homotopy-theoretic model for the Bott spiral of symmetry-protected topological phases (SPTs) studied by Queiroz--Khalaf--Stern. We model free and interac…
A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories
Cameron Krulewski, Lukas Müller, Luuk Stehouwer
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'…
Free phases of Majorana fermions: Tenfold ways compared
Luuk Stehouwer
We provide a mathematically rigorous classification of symmetry-protected topological (SPT) phases of neutral free fermions. Our approach utilizes Karoubi triples with negative squ…
Is Crane--Yetter fully extended?
Luuk Stehouwer
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifi…
The spin-statistics theorem for topological quantum field theories
Luuk Stehouwer
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represe…