Gravitational anomalies in a dispersive approach

TL;DR

This paper demonstrates that gravitational anomalies in two dimensions, such as Einstein and Weyl anomalies, can be fully characterized using dispersion relations, highlighting their infrared origin and singular behavior at zero momentum.

Contribution

It introduces a dispersive approach to determine gravitational anomalies, emphasizing their infrared features and singularities, providing a new perspective on anomaly calculation.

Findings

Anomalies originate from infrared features of formfactors.

Imaginary parts approach delta-function singularity at zero momentum.

Dispersion relations fully determine the gravitational anomalies.

Abstract

The gravitational anomalies in two dimensions, specifically the Einstein anomaly and the Weyl anomaly, are fully determined by means of dispersion relations. In this approach the anomalies originate from the peculiar infrared feature of the imaginary part of the relevant formfactor which approaches a $\delta$-function singularity at zero momentum squared when $m \to 0$.