The phase diagram of four-dimensional Einstein-Hilbert gravity is studied using Wilson's renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed. arXiv:1209.4038v1 [hep-th]

We study four-dimensional quantum gravity using non-perturbative renormalization group methods. We solve the corresponding equations for the fully momentum-dependent propagator, Newtons coupling and the cosmological constant. For the first time, we obtain a global phase diagram where the non-Gaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to a classical infrared fixed point. The theory is therefore ultraviolet complete and deforms smoothly into classical gravity as the infrared limit is approached.

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. The logarithmic divergencies give rise to an extended effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six. In the pure Yang-Mills sector this counterterm can be removed by a nonlinear field redefinition of the gauge potential, reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in the background field method with dimensional regularization.PACS numbers: 12.10. Kt, 11.10.Hi Perturbatively quantized general relativity is well known to be a non-renormalizable theory due to the negative mass dimension of its coupling constant κ [1]. The coupling to matter fields does generically not improve the situation [1,2,3], although the possibility of perturbative finiteness of the maximally supersymmetric gravity theory is still open [4]. Hence, Einstein's theory of gravity does not constitute a fundamental theory as its non-renormalizability necessitates the inclusion of an infinite set of higher dimension counterterms in the perturbative quantization process. Nevertheless, as advocated by Donoghue [5], it may be treated as an approximation to a fundamental theory of quantum gravity by the methodology of effective field theories in order to describe interactions at scales well below the Planck mass M P ∼ 1/κ ∼ 10 19 GeV.In an interesting recent paper Robinson and Wilczek [6] reported on a calculation in Einstein gravity coupled to Yang-Mills theory, where the quantum gravity contributions to the running of the Yang-Mills coupling g were investigated at one-loop order. Interestingly a negative gravitational contribution to the Callan-Symanzik β function, which quantifies the flow of the Yang-Mills coupling with the energy scale E, was foundwith a 0 = −3/2 in our conventions for the gravitational coupling κ 2 , see (2). Irrespective of the non-gravitational value of b 0 this would render any gauge theory assymptotically free at energies E close to the Planck mass (including e.g. pure U (1) Maxwell theory). Responsible for this effect were quadratic divergencies in one-loop graphs containing the graviton propagator [7]. As a number of discussed scenarios of physics beyond the standard model contain higher dimensional gravity theories with small gravitational scales, such an effect might be observable at the Large Hadron Collider, as was qualitatively studied in [8].However, two recent works have cast doubts on the results of [6] by reconsidering this effect in Einstein-Maxwell theory. The authors of [6] u...

We propose a simple fixed-point scenario in the renormalization flow of a scalar dilaton coupled to gravity. This would render gravity non-perturbatively renormalizable and thus constitute a viable theory of quantum gravity. On the fixed point dilatation symmetry is exact and the quantum effective action takes a very simple form. Realistic gravity with a nonzero Planck mass is obtained through a nonzero expectation value for the scalar field, constituting a spontaneous scale symmetry breaking. Furthermore, relevant couplings for the flow away from the fixed point can be associated with a "dilatation anomaly" that is responsible for dynamical dark energy. For the proposed fixed point and flow away from it the cosmological "constant" vanishes for asymptotic time.

We consider the lowest order quantum gravitational corrections to Yukawa and phi{4} interactions. Our results show that quantum gravity leads to contributions to the running coupling constants if the particles are massive and therefore alters the scaling behavior of the standard model. Furthermore, we find that the gravitational contributions to the running of the masses vanish.