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Conformal quantum gravity with the Gauss-Bonnet term

Jul, 2003

21 pages

Published in:

Phys.Rev.D 70 (2004) 044024

e-Print:

hep-th/0307030 [hep-th]

DOI:

10.1103/PhysRevD.70.044024

Report number:

DF-UFJF-03-07

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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-\epsilon

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

04.60.-m
04.50.+h
11.10.Hi
quantum gravity: Weyl
invariance: conformal
Gauss-Bonnet term
perturbation theory: higher-order
renormalization group: fixed point
quantization
gauge fixing: dependence

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