ANOMALIES OF ARBITRARY GAUGE GROUP AND ITS REDUCTION GROUP, EINSTEIN AND LORENTZ ANOMALIES

Based upon the properties of the characteristic classes and their Chern-Simons secondary characteristic classes, the “Abelian” anomalies in M²ⁿ⁺², the Euler-Heisenberg effective actions in M²ⁿ⁺¹, as well as the non-Abelian anomalies in M²ⁿ for arbitrary gauge group and its reduction subgroup have been investigated thoroughly and the application to the gravitational anomalies is made. It is shown that the “Abelian” anomalies of such groups are equal to each other, their Euler-Heisenberg actions are also closely related to each other, and their non-Abelian anomalies are also equivalent if their common generating functional can be taken as a counter-term. For the gravitational anomalies we present the common generating functional for both non-Abelian Einstein and Lorentz anomalies in M⁴ⁿ⁺² and show the relationship between them.