Weinberg’s asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gaussian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gaussian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the long-standing criticism that asymptotic safety will not survive once a “proper perturbative counterterm” is included in the projection space.

We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional renormalization group scheme, the anomalous dimension ${\eta }_c$ is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of ${\eta }_c\simeq -0.78$ for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point values for the gravitational coupling and cosmological constant and the associated critical exponents; also their gauge dependence is slightly reduced. Our results provide further evidence for the asymptotic-safety scenario of quantum gravity. DOI: http://dx.doi.org/10.1103/PhysRevD.81.104010 © 2010 The American Physical Society

Electron-positron pair production in oscillating electric fields is investigated in the nonperturbative threshold regime. Accurate numerical solutions of quantum kinetic theory for corresponding observables are presented and analyzed in terms of a proposed model for an effective mass of electrons and positrons acquired within the given strong electric field. Although this effective mass cannot provide an exact description of the collective interaction of a charged particle with the strong field, physical observables are identified which carry direct and sensitive signatures of the effective mass.

We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irre-ducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields.