Differential geometry construction of anomalies and topological invariants in various dimensions

TL;DR

This paper introduces a geometric framework for constructing gauge-invariant and non-invariant topological densities and anomalies in various dimensions, extending classical invariants like Pontryagin and Chern-Simons forms.

Contribution

It develops a differential geometry approach to derive new metric-independent densities and secondary forms in extended non-Abelian tensor gauge theories, revealing potential gauge anomalies.

Findings

Identified new gauge-invariant densities in various dimensions.

Constructed secondary characteristic forms related to these densities.

Compared transformations of these forms with classical Chern-Simons forms.

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.