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Conformal Quantum Gravity with the Gauss-Bonnet Term

G. de Berredo-Peixoto·I. L. Shapiro
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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 $n=4-ε$ manifest new fixed points due to quantum effects of this term.

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G. de Berredo-Peixoto, I. L. Shapiro. 2004-06-16. Conformal Quantum Gravity with the Gauss-Bonnet Term. https://doi.org/10.1103/physrevd.70.044024

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