A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.
Explicit cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf-Witten invariants
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abstract
We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf-Witten Invariants of the $n$-torus for all $n$.
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hep-th 1years
2026 1verdicts
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Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.