Conformal Quantum Gravity with the Gauss-Bonnet Term

TL;DR

This paper explores the impact of the Gauss-Bonnet term in conformal quantum gravity, revealing its topological nature in four dimensions and its dynamical role in other dimensions, with implications for quantum fixed points.

Contribution

It provides a detailed analysis of the Gauss-Bonnet term's role in conformal quantum gravity across different dimensions, clarifying its topological and dynamical aspects.

Findings

Gauss-Bonnet term cancels in 4D, confirming its topological nature.

In dimensions other than 4, the Gauss-Bonnet term influences quantum behavior.

New fixed points emerge in the renormalization group flow due to the Gauss-Bonnet term.

Abstract

The conformal gravity is one of the most important models of quantum gravity with higher derivatives. We investigate the role of the Gauss-Bonnet term in this theory. The coincidence limit of the second coefficient of the Schwinger-DeWitt expansion is evaluated in an arbitrary dimension $n$. In the limit $n=4$ the Gauss-Bonnet term is topological and its contribution cancels. This cancellation provides an efficient test for the correctness of calculation and, simultaneously, clarifies the long-standing general problem concerning the role of the topological term in quantum gravity. For $n\neq 4$ the Gauss-Bonnet term becomes dynamical in the classical theory and relevant at the quantum level. In particular, the renormalization group equations in dimension $n=4-\epsilon$ manifest new fixed points due to quantum effects of this term.