Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2021)066
Keywords
Chern-Simons Theories; Differential and Algebraic Geometry; Gauge Symmetry
Categories
Funding
- bilateral DAAD-CONICYT [62160015]
- Max-Planck-Society
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A free differential algebra extends the structure of a Lie algebra by including new Maurer-Cartan equations for higher-degree differential forms. This article proposes a generalization of the Chern-Weil theorem for free differential algebras with only one p-form extension, achieved through a generalization of the covariant derivative. The study also investigates the potential existence of anomalies and analyzes properties and particular cases.
A free differential algebra is generalization of a Lie algebra in which the mathematical structure is extended by including of new Maurer-Cartan equations for higher-degree differential forms. In this article, we propose a generalization of the Chern-Weil theorem for free differential algebras containing only one p-form extension. This is achieved through a generalization of the covariant derivative, leading to an extension of the standard formula for Chern-Simons and transgression forms. We also study the possible existence of anomalies originated on this kind of structure. Some properties and particular cases are analyzed.
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