Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-07-02
Phys.Rev. D70 (2004) 044024
Physics
High Energy Physics
High Energy Physics - Theory
17 pages. Improved version. Analysis of the renormalization group in 4-epsilon extended. RevTeX4. Accepted in Physical Review
Scientific paper
10.1103/PhysRevD.70.044024
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.
Berredo-Peixoto Guilherme de
Shapiro Ilya L.
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