Anomalies and gravity

TL;DR

This paper reviews anomalies in gauge theories of gravity, focusing on the relationship between spin, axial current, and gauge spin, and discusses their implications for quantum gravity approaches.

Contribution

It clarifies the form of chiral anomalies in gravitational gauge theories and explores their relevance to Ashtekar's quantum gravity framework.

Findings

Only generalized U(1)-Pontrjagin forms appear in the chiral anomaly with gravity.

Diagrammatic techniques reveal the structure of anomalies in these theories.

Implications for canonical quantum gravity approaches are discussed.

Abstract

Anomalies in Yang-Mills type gauge theories of gravity are reviewed. Particular attention is paid to the relation between the Dirac spin, the axial current j_5 and the non-covariant gauge spin C. Using diagrammatic techniques, we show that only generalizations of the U(1)- Pontrjagin four--form F^ F= dC arise in the chiral anomaly, even when coupled to gravity. Implications for Ashtekar's canonical approach to quantum gravity are discussed.