# Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure

@inproceedings{Lauscher2005AsymptoticSI, title={Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure}, author={Oliver Lauscher and Martin Reuter}, year={2005} }

The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic safety implies that spacetime is a fractal in general, with a fractal dimension of 2 on sub-Planckian length scales.

## Figures from this paper

## 37 Citations

Quantum Einstein gravity

- Physics
- 2012

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,…

The Asymptotic Safety Scenario in Quantum Gravity

- Physics, MedicineLiving reviews in relativity
- 2006

Criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented and self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

TOPICAL REVIEW: The asymptotic safety scenario in quantum gravity: an introduction

- Physics
- 2006

The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings…

Scale-dependent metric and causal structures in Quantum Einstein Gravity

- Physics
- 2007

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective…

Gravity, Geometry and the Quantum

- Physics
- 2006

After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is…

Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry

- Mathematics, Physics
- 2007

Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight…

Can we see quantum gravity? Photons in the asymptotic-safety scenario

- Physics
- 2012

A bstractIn the search for a quantum theory of gravity it is crucial to find experimental access to quantum gravitational effects. Since these are expected to be very small at observationally…

An introduction to quantum gravity

- Physics
- 2008

Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight…

El Naschie’s Cantorian gravity and Einstein’s quantum gravity

- Physics
- 2006

Abstract A geometric formulation of the gravitation theory on a fractal space–time is given. Then, a connection is introduced on a tangent bundle, the connection coefficients, the Riemann curvature…

Nonperturbative sum over topologies in 2D Lorentzian quantum gravity

- Physics
- 2006

The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in…

## References

SHOWING 1-10 OF 92 REFERENCES

Fractal spacetime structure in asymptotically safe gravity

- Physics
- 2005

Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-planckian distances it predicts that…

Is quantum Einstein gravity nonperturbatively renormalizable

- Physics
- 2002

We find considerable evidence supporting the conjecture that four-dimensional quantum Einstein gravity is 'asymptotically safe' in Weinberg's sense. This would mean that the theory is likely to be…

Proper time flow equation for gravity

- Physics
- 2005

We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact…

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

- Physics
- 2002

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…

Non-Trivial Ultraviolet Fixed Point in Quantum Gravity

- Physics
- 1999

The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions (2 � d ≤ 4). It is shown that the ultraviolet…

A Proper time cure for the conformal sickness in quantum gravity

- Physics
- 2001

Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically…

A minimal length from the cutoff modes in asymptotically safe quantum gravity

- Physics
- 2006

Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into…

Fixed points of quantum gravity

- Physics
- 2004

Euclidean quantum gravity is studied with renormalization group methods. Analytical results for a nontrivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameters in…

Emergence of a 4D world from causal quantum gravity.

- Physics, MedicinePhysical review letters
- 2004

Evidence is presented that a macroscopic four-dimensional world emerges from Causal Dynamical Triangulations in four dimensions dynamically, which provides a background-independent definition of the sum over geometries in nonperturbative quantum gravity.

Renormalization Group and Quantum Gravity

- Physics
- 1990

Abstract We study non-perturbative effects of the quantum fluctuation of gravity by means of the ϵ-expansion around two dimensions and the renormalization group method. By introducing the fractal…