New gauge anomalies and topological invariants in various dimensions
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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, which we compare with the corresponding transformations of the Chern–Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.
KeywordsGauge Transformation Gauge Field Gauge Parameter Invariant Density Gauge Variation
One of us G.S. would like to thank Ludwig Faddeev, Luis Alvarez-Gaume and Raymond Stora for stimulating discussions and CERN Theory Division, where part of this work was completed, for hospitality. This work was supported in part by the European Commission under the ERC Advanced Grant 226371 and the contract PITN-GA-2009-237920.
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