Frank Saueressig

Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation

The exact renormalization group equation for pure quantum gravity is used to derive the nonperturbative \ensuremath{\beta}-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with a sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in

Quantum Einstein gravity

d=4.

Asymptotic safety in higher-derivative gravity

The resulting renormalization group trajectories are classified and their physical relevance is discussed. The nontrivial fixed point which, if present in the exact theory, might render quantum Einstein gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.

Bimetric renormalization group flows in 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 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.

Fractal space-times under the microscope: a renormalization group view on Monte Carlo data

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

Matter induced bimetric actions for gravity

Abstract The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.

Special geometry of euclidean supersymmetry II. Hypermultiplets and the c-map

A bstractThe emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension ds and walk dimension dw associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where ds = d, dw = 2, a semi-classical regime where ds = 2d/(2 + d), dw = 2 + d, and the UV-fixed point regime where ds = d/2, dw = 4. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.

Asymptotically Safe Lorentzian Gravity

Abstract The gravitational effective average action is studied in a bimetric truncation with a nontrivial background field dependence, and its renormalization group flow due to a scalar multiplet coupled to gravity is derived. Neglecting the metric contributions to the corresponding beta functions, the analysis of its fixed points reveals that, even on the new enlarged theory space which includes bimetric action functionals, the theory is asymptotically safe in the large N expansion.

Ghost wavefunction renormalization in asymptotically safe quantum gravity

We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in euclidean theories with rigid Script

Probing the quantum nature of spacetime by diffusion

N = 2