On the local term in the anomaly-induced action of Weyl quantum gravity

TL;DR

This paper investigates the local term in the anomaly-induced action of Weyl quantum gravity, focusing on the $R^2$-term and its relation to the conformal anomaly, using heat kernel techniques for precise calculation.

Contribution

It provides a detailed calculation and confirmation of the local $R^2$-term in the anomaly-induced action of Weyl quantum gravity using advanced heat kernel methods.

Findings

Confirmed the form of the $R^2$-term in the effective action.

Validated heat kernel techniques for higher-derivative operators.

Clarified the relation between the $R^2$-term and conformal anomaly.

Abstract

The finite local conformally non-invariant $R^2$-term emerges in the one-loop effective action of the model of quantum gravity based on the Weyl-squared classical action. This term is related to the $\Box R$ contribution to the conformal anomaly, which in a wide class of regularization schemes is determined by the second Schwinger-DeWitt (or Gilkey-Seeley) coefficient of the heat kernel expansion for inverse propagators of the theory. The calculation of this term requires evaluating the contributions of the fourth-order derivative minimal and of the second-order nonminimal operators in the tensor and vector sectors of the theory, corresponding to metric, ghost and gauge-fixing operators. To ensure the correctness of existing formulas, we derived (and confirmed) the result using a special technique of calculations, based on the heat-kernel representation of the Euclidean Green's function and the method of universal functional traces.