Gravitational anomalies of fermionic higher-spin fields

TL;DR

This paper uses the Atiyah-Singer index theorem to compute gravitational anomalies for fermionic higher-spin fields across multiple dimensions, revealing anomaly cancellations for an infinite tower of fields with alternating chiralities.

Contribution

It provides a formal computation of gravitational anomalies for higher-spin fermionic fields in various dimensions using topological methods.

Findings

Anomaly cancellations occur for an infinite tower of fields with alternating chiralities.

Explicit calculations of gravitational anomalies in 2, 6, and 10 dimensions.

U(1) mixed gauge-gravitational anomaly computed in four dimensions.

Abstract

Using the Atiyah-Singer index theorem, we formally compute gravitational anomalies for fermionic higher-spin fields in two, six and ten dimensions, as well as the U(1) mixed gauge-gravitational anomaly in four dimensions. In all cases, anomaly cancellations are found for an infinite tower of fields with alternating chiralities.