Conformal quantum gravity with the Gauss-Bonnet term

Abstract

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 nϭ4 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 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 ϭ4Ϫ⑀ manifest new fixed points due to quantum effects of this term.

Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

“…If one attempts to fix the problem by introducing the special renormalization condition, the theory becomes conformally non-invariant already at the classical level. In this respect the theory of conformal scalar field is closer to quantum conformal gravity [23], rather than to the theory of free conformal matter on purely metric background.…”

“…In the last case the anomaly corresponds to the local d 4 x √ gR 2 term in the effective action, and therefore the arbitrariness in the anomaly corresponds to the freedom of adding a local finite d 4 x √ gR 2 term to the classical vacuum action. In the present case the anomalous contribution corresponds to the finite term √ gR 2 term in conformal quantum gravity [23] rather than in the semiclassical theory. From the previous discussions it is also straightforward to understand what is the general structure of the ambiguous terms in any dimension: ✷φ 2 and R in two dimensions and furthermore…”

Local Conformal Symmetry and its Fate at Quantum Level

“…The derivation of the one-loop divergences in the conformal theory has been performed in [36,40,41]. The result obtained in [41] with the method including rigid automatic control of the calculations fits with the previous ones and has the form…”

“…The result obtained in [41] with the method including rigid automatic control of the calculations fits with the previous ones and has the form…”

On the conformal properties of topological terms in even dimensions

“…Previously, the last case has been discussed in some works devoted to quantum gravity [16,17], where one can find more detailed consideration.…”