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.
The role of p_1-structures in 3-dimensional Chern-Simons theories
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Our recent paper~\cite{FST} with Claudia Scheimbauer uses the cobordism hypothesis to construct fully local Chern-Simons theories. Here we expose some physics motivations: Yang-Mills plus Chern-Simons in the bosonic case and the free Majorana-Weyl spinor field in the fermionic case. We also give expositions of tangential structures and invertible field theories, in particular the 'gravitational Chern-Simons theory' used by Witten to obtain topological field theories from the physical theories.
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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.