Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.
Boyle Smith and J
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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.
citing papers explorer
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Dai-Freed anomalies and level matching in heterotic asymmetric orbifolds
Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.
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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.