Universal bundle for gravity, local index theorem, and covariant gravitational anomalies

Details Universal bundle for gravity, local index theorem, and covariant gravitational anomalies Universal bundle for gravity, local index theorem, and covariant gravitational anomalies

1993-09-03

arxiv.org/abs/hep-th/9309020v1

J.Math.Phys. 35 (1994) 5945-5968

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LMU-TPW 93-16, typeset by amstex

Scientific paper

10.1063/1.530721

Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of the local index theorem for families of Bismut and Freed the consistent gravitational anomalies are calculated. Covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant Schwinger terms is derived. The relation between consistent and covariant anomalies is studied. Finally a geometrical realization of the gravitational BRS, anti-BRS transformations is presented which enables the formulation of a kind of covariance condition for covariant gravitational anomalies.

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