Differential geometry construction of anomalies and topological invariants in various dimensions

Abstract

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.

arXiv comment27 pages, references added, matches published version

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• Extended gauge theory and gauged Free Differential Algebras
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• Modified newtonian dynamics and non-relativistic ChSAS gravity
• Non-Abelian tensor gauge fields and new topological invariants
• On the $L_{\infty }$ formulation of Chern-Simons theories
• Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory
• Gauge-invariant theories and higher-degree forms