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Explores the construction of local Chern–Simons theories, suggesting deeper connections among gauge theories.
Our recent paper [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 underlying gauge theory.
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Freed et al. (2026) studied this question.
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