Covariant Lagrangian Formulation of Chern-Simons and BF Theories

TL;DR

This paper develops a covariant Lagrangian framework for Chern-Simons theories in arbitrary odd dimensions, enabling comparison with BF theories and extending understanding of their geometric and topological properties.

Contribution

It introduces a covariant formulation of higher-dimensional Chern-Simons theories using a vacuum connection, linking them to BF theories and providing explicit field equations and conserved quantities.

Findings

Derived covariant field equations and Noether currents for Chern-Simons theories.

Established a clear relation between Chern-Simons and BF theories in higher dimensions.

Provided a unified geometric framework for analyzing topological gauge theories.

Abstract

We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed so that results are easily compared with the well-known results in dimension 3. Finally we use this covariant formulation of Chern-Simons theories to investigate their relation with topological BF theories.