Higher Chern-Simons based on (2-)crossed modules
Danhua Song, Mengyao Wu, Ke Wu, Jie Yang
TL;DR
This paper develops higher Chern-Simons theories using (2-)crossed modules, introducing generalized connections and forms, and establishing related Chern-Weil theorems for advanced gauge theories.
Contribution
It introduces a novel framework for higher Chern-Simons theories based on (2-)crossed modules, expanding the mathematical foundation of gauge theories.
Findings
Defined generalized connections with higher connections
Constructed higher Chern-Simons actions from generalized forms
Developed higher second Chern forms and proved Chern-Weil theorems
Abstract
We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher connections. Then we establish the generalized Chern-Simons forms to get the higher Chern-Simons actions. Finally, we develop the higher second Chern forms and Chern-Weil theorems.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis