Locality and universality in gravitational anomaly cancellation

TL;DR

This paper establishes conditions for gravitational anomaly cancellation, showing perturbative anomalies cannot be canceled, but global anomalies in certain dimensions can, with Chern-Simons counterterms being the unique solution, and explores the link between locality and universality.

Contribution

It provides necessary and sufficient conditions for anomaly cancellation and identifies Chern-Simons terms as the unique method for canceling global anomalies in specific dimensions.

Findings

Perturbative gravitational anomalies cannot be canceled.

Global anomalies in dimensions not congruent to 3 mod 4 cannot be canceled.

In dimensions 3 mod 4, global anomalies can be canceled using Chern-Simons counterterms.

Abstract

We obtain necesary and sufficient conditions for gravitational anomaly cancellation. We show that perturbative gravitational anomalies can never be cancelled. In a similar way, in dimensions $n\neq3\operatorname{mod}4$ it is impossible to cancell global anomalies. However, in dimensions $n=3\operatorname{mod}4$ global anomalies can be cancelled. We prove that the unique way to cancel the anomaly is by using a Chern-Simons counterterm. Furthermore, the relationship between the problems of locality and universality is analyzed for gravitational anomalies.