Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
Bosonic Topological Insulators and Paramagnets: a view from cobordisms
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We classify Bosonic Topological Insulators and Paramagnets in D<=4 spatial dimensions using the cobordism approach. For D<4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state. For D=4 there is a unique "beyond group cohomology" phase. It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.
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Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
citing papers explorer
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$K$-Theoretic Obstructions to Linearizing QCA Representations
Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
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Gauging in superconductors and other electronic systems
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.