Question on the Existence of Gravitational Anomalies

TL;DR

This paper critically examines claims of gravitational anomalies, clarifies the distinction between T-product and T*-product quantities, and demonstrates the non-existence of such anomalies in 2D quantum gravity when calculations are properly conducted.

Contribution

It clarifies the role of T*-product quantities in gravitational anomaly calculations and explicitly shows the non-existence of anomalies in 2D quantum gravity.

Findings

Energy-momentum tensor conservation in 2D quantum gravity

Non-existence of gravitational anomalies in the examined framework

Importance of correctly handling T*-product quantities

Abstract

The existence of gravitational anomalies claimed by Alvarez-Gaume and Witten is examined critically. It is pointed out that they were unaware of the essential difference between T-product quantities and T*-product quantities. Field equations and, therefore, the Noether theorem are, in general, violated in the case of T*-product quantities, that is, those directly calculable from Feynman integrals. In the 2-dimensional case, it is explicitly confirmed that the energy-momentum tensor is strictly conserved if the above stated property of the T*-product quantities is correctly taken into account. The non-existence of gravitational anomalies is explicitly demonstrated for the BRS-formulated 2-dimensional quantum gravity in the Heisenberg picture.