The role of p_1-structures in 3-dimensional Chern-Simons theories

TL;DR

This paper explores the mathematical structures underlying 3D Chern-Simons theories, connecting cobordism hypothesis, tangential structures, and physical motivations like Yang-Mills and Majorana-Weyl fields.

Contribution

It applies the cobordism hypothesis to construct local Chern-Simons theories and discusses their physical motivations and related structures.

Findings

Construction of fully local Chern-Simons theories using cobordism hypothesis

Exposition of physical motivations including Yang-Mills and Majorana-Weyl fields

Discussion of gravitational Chern-Simons theory and invertible field theories

Abstract

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.