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

TL;DR

This paper explores the geometric structure of the universal bundle for gravity to analyze and relate consistent and covariant gravitational anomalies using index theorems and secondary characteristic classes.

Contribution

It constructs the universal bundle for gravity and derives new descent equations linking covariant anomalies with secondary characteristic classes.

Findings

Explicit construction of the universal bundle for gravity.

Calculation of consistent gravitational anomalies via local index theorem.

Derivation of new descent equations for covariant anomalies.

Abstract

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.