Ultraviolet properties of f(R)-Gravity

We discuss the existence and properties of a nontrivial fixed point in f(R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizabile.Comment: 4 page

Fluid Membranes and 2d Quantum Gravity

We study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms we derive a system of beta functions for the running surface tension, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at $T\neq0$. Finally, we propose to identify the $D\rightarrow 0$ limit of the theory with two dimensional quantum gravity. In this limit we derive new beta functions for both cosmological and Newton's constants.Comment: 16 pages, 1 figur

One-loop effective action in quantum gravitation

We present the formalism of computing one-loop effective action for Quantum Gravitation using non-local heat kernel methods. We found agreement with previous old results. In main part of my presentation I considered the system of E-H gravitation and scalar fields. We were able to derive non-local quantum effective action up to the second order in heat kernel generalized curvatures. By going to flat spacetime expressions for gravitational form factors are possible to construct and compare with the results from effective field theory for gravity

The electroweak S and T parameters from a fixed point condition

We consider the standard model without the Higgs boson, where the Goldstone modes are described by a nonlinear sigma model. We study the renormalization group flow of the sigma model coupling f and of the electroweak parameters S and T. The condition that the couplings reach a fixed point at high energy leaves the low energy values of f and T arbitrary (to be determined experimentally) and fixes S to a value compatible with electroweak precision data.Comment: 4 pages, 2 figure

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

Geometry of the quantum universe

A universe much like the (Euclidean) de Sitter space-time appears as background geometry in the causal dynamical triangulation (CDT) regularization of quantum gravity. We study the geometry of such universes which appear in the path integral as a function of the bare coupling constants of the theory.Comment: 19 pages, 7 figures. Typos corrected. Conclusions unchange

Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization

We compute the scale-dependence of the Planck mass and of the vacuum expectation value of the Higgs field using two very different renormalization group methods: a "holographic" procedure based on Einstein's equations in five dimensions with matter confined to a 3-brane, and a "functional" procedure in four dimensions based on a Wilsonian momentum cutoff. Both calculations lead to very similar results, suggesting that the coupled theory approaches a non-trivial fixed point in the ultraviolet.Comment: 11 pages, 1 figur

Exact Curie temperature for the Ising model on Archimedean and Laves lattices

Using the Feynman-Vdovichenko combinatorial approach to the two dimensional Ising model, we determine the exact Curie temperature for all two dimensional Archimedean lattices. By means of duality, we extend our results to cover all two dimensional Laves lattices. For those lattices where the exact critical temperatures are not exactly known yet, we compare them with Monte Carlo simulations.Comment: 10 pages, 1 figures, 3 table

CDT meets Horava-Lifshitz gravity

The theory of causal dynamical triangulations (CDT) attempts to define a nonperturbative theory of quantum gravity as a sum over space-time geometries. One of the ingredients of the CDT framework is a global time foliation, which also plays a central role in the quantum gravity theory recently formulated by Ho\v{r}ava. We show that the phase diagram of CDT bears a striking resemblance with the generic Lifshitz phase diagram appealed to by Ho\v{r}ava. We argue that CDT might provide a unifying nonperturbative framework for anisotropic as well as isotropic theories of quantum gravity.Comment: 17 pages, 3 figures. Typos corrected, a few remarks added

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

The 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 $d_s$ and walk dimension $d_w$ 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 $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. 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.Comment: 26 pages, 6 figure