Consistent gravitational anomalies for chiral scalars

TL;DR

This paper derives the exact consistent gravitational anomaly for chiral scalars using two methods: Schwinger-DeWitt regularization and cohomological techniques, providing insights into anomalies in curved spacetime.

Contribution

It presents two novel derivations of the gravitational anomaly for chiral scalars, enhancing understanding of anomalies in two-dimensional quantum field theories.

Findings

Derived the anomaly via Schwinger-DeWitt regularization.

Used cohomological methods to obtain the anomaly.

Confirmed the consistency of the gravitational anomaly in curved space.

Abstract

Starting from the Henneaux-Teitelboim action for a chiral scalar, which generalizes to curved space the Floreanini-Jackiw action, we give two simple derivations of the exact consistent gravitational anomaly. The first derivation is through the Schwinger-DeWitt regularization. The second exploits cohomological methods and uses the fact that in dimension two the diffeomorphism transformations are described by a single ghost which allows to climb the cohomological chain in a unique way.