Abstract
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky–Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive ghost-like states at the tree-level.
Highlights
The calculation of quantum corrections always had a very special role in quantum theories of gravity
Later on one could learn a lot from the two-loop calculations in general relativity [5,6]
By dimensional reasons similar to the ones that lead to (1), one can show that the beta function for the inverse Newton constant should be proportional to the ratios ωN−1,i /ωN, j, where i, j = (R, C, GB) for N 2
Summary
The calculation of quantum corrections always had a very special role in quantum theories of gravity. There exists a class of nonlocal theories in which UV behaviour is exactly the same like in polynomial higher derivative theories They satisfy the above three points, namely they are quantum super-renormalizable unitary models and the analysis of divergences and RG running presented here apply to these theories as well. It turns out that the derivation of one-loop divergences by taking a limit in the results for a polynomial models meets serious difficulties, which can be solved only for a special class of nonlocal theories, which are asymptotically polynomial in the ultraviolet regime. Still these theories are super-renormalizable or even finite.
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