Non-perturbative QEG Corrections to the Yang-Mills Beta Function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. Our result is consistent with the conjecture that Quantum Einstein Gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.Comment: To appear in the proceedings of CORFU 200

Running Gauge Coupling in Asymptotically Safe Quantum Gravity

We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page

Quantum Einstein Gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravit

Renormalization Group Flow in Scalar-Tensor Theories. II

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.Comment: 14 pages. v.2: Minor changes, some references adde

Infrared fixed point in quantum Einstein gravity

We performed the renormalization group analysis of the quantum Einstein gravity in the deep infrared regime for different types of extensions of the model. It is shown that an attractive infrared point exists in the broken symmetric phase of the model. It is also shown that due to the Gaussian fixed point the IR critical exponent $\nu$ of the correlation length is 1/2. However, there exists a certain extension of the model which gives finite correlation length in the broken symmetric phase. It typically appears in case of models possessing a first order phase transitions as is demonstrated on the example of the scalar field theory with a Coleman-Weinberg potential.Comment: 9 pages, 7 figures, final version, to appear in JHE

QED coupled to QEG

We discuss the non-perturbative renormalization group flow of Quantum Electrodynamics (QED) coupled to Quantum Einstein Gravity (QEG) and explore the possibilities for defining its continuum limit at a fixed point that would lead to a non-trivial, i.e. interacting field theory. We find two fixed points suitable for the Asymptotic Safety construction. In the first case, the fine-structure constant vanishes at the fixed point and its infrared ("renormalized") value is a free parameter not determined by the theory itself. In the second case, the fixed point value of the fine-structure constant is non-zero, and its infrared value is a computable prediction of the theory.Comment: 25 pages, 3 figure

Quantum gravity effects in Myers-Perry space-times

We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton's coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions