122 research outputs found

### Nonlocal Quantum Gravity and the Size of the Universe

Motivated by the conjecture that the cosmological constant problem is solved
by strong quantum effects in the infrared we use the exact flow equation of
Quantum Einstein Gravity to determine the renormalization group behavior of a
class of nonlocal effective actions. They consist of the Einstein-Hilbert term
and a general nonlinear function $F_k(V)$ of the Euclidean spacetime volume
$V$. For the $V + V \ln V$-invariant the renormalization group running
enormously suppresses the value of the renormalized curvature which results
from Planck-size parameters specified at the Planck scale. One obtains very
large, i.e., almost flat universes without finetuning the cosmological
constant. A critical infrared fixed point is found where gravity is scale
invariant.Comment: 6 pages, 1 figure, contribution to the proceedings of the 36th
International Symposium Ahrenshoop, Berlin, August 26-30, 200

### Impact of topology in foliated Quantum Einstein Gravity

We use a functional renormalization group equation tailored to the
Arnowitt-Deser-Misner formulation of gravity to study the scale-dependence of
Newton's coupling and the cosmological constant on a background spacetime with
topology S^1xS^d. The resulting beta functions possess a non-trivial
renormalization group fixed point, which may provide the high-energy completion
of the theory through the asymptotic safety mechanism. The fixed point is
robust with respect to changing the parametrization of the metric fluctuations
and regulator scheme. The phase diagrams show that this fixed point is
connected to a classical regime through a crossover. In addition the flow may
exhibit a regime of "gravitational instability", modifying the theory in the
deep infrared. Our work complements earlier studies of the gravitational
renormalization group flow on a background topology S^1xT^d and establishes
that the flow is essentially independent of the background topology.Comment: 33 pages, 14 figure

### Asymptotic safety in higher-derivative gravity

We study the non-perturbative renormalization group flow of higher-derivative
gravity employing functional renormalization group techniques. The
non-perturbative contributions to the $\beta$-functions shift the known
perturbative ultraviolet fixed point into a non-trivial 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.Comment: 8 pages; 1 figure; revised versio

### On the scaling of composite operators in Asymptotic Safety

The Asymptotic Safety hypothesis states that the high-energy completion of
gravity is provided by an interacting renormalization group fixed point. This
implies non-trivial quantum corrections to the scaling dimensions of operators
and correlation functions which are characteristic for the corresponding
universality class. We use the composite operator formalism for the effective
average action to derive an analytic expression for the scaling dimension of an
infinite family of geometric operators $\int d^dx \sqrt{g} R^n$. We demonstrate
that the anomalous dimensions interpolate continuously between their fixed
point value and zero when evaluated along renormalization group trajectories
approximating classical general relativity at low energy. Thus classical
geometry emerges when quantum fluctuations are integrated out. We also compare
our results to the stability properties of the interacting renormalization
group fixed point projected to $f(R)$-gravity, showing that the composite
operator formalism in the single-operator approximation cannot be used to
reliably determine the number of relevant parameters of the theory.Comment: matches published versio

### Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the
gravitational renormalization group flow in the Einstein-Hilbert truncation
supplemented by the wave-function renormalization of the ghost fields. The
latter induces non-trivial corrections to the beta-functions for Newton's
constant and the cosmological constant. The resulting ghost-improved phase
diagram is investigated in detail. In particular, we find a non-trivial
ultraviolet fixed point in agreement with the asymptotic safety conjecture,
which also survives in the presence of extra dimensions. In four dimensions the
ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting
space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 figure

### Membrane and fivebrane instantons from quaternionic geometry

We determine the one-instanton corrections to the universal hypermultiplet moduli space coming both from Euclidean membranes and NS-fivebranes wrapping the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely encoded by a single function characterizing a generic four-dimensional quaternion-Kahler metric without isometries. We give explicit solutions for this function describing all one-instanton corrections, including the fluctuations around the instanton to all orders in the string coupling constant. In the semi-classical limit these results are in perfect agreement with previous supergravity calculations

### A proper fixed functional for four-dimensional Quantum Einstein Gravity

Abstract: Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory’s renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f(R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R2, dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed

### On the renormalization group flow of f(R)-gravity

We use the functional renormalization group equation for quantum gravity to
construct a non-perturbative flow equation for modified gravity theories of the
form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain
gravitational interactions monomials can be consistently decoupled from the
renormalization group (RG) flow and reproduce recent results on the asymptotic
safety conjecture. The non-perturbative RG flow of non-local extensions of the
Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int
d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of
such interactions resolves the infrared singularities plaguing the RG
trajectories with positive cosmological constant in previous truncations. In
particular, in some $R^{-n}$-truncations all physical trajectories emanate from
a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG
flow of the $\ln(R)$-truncation contains an infrared attractor which drives a
positive cosmological constant to zero dynamically.Comment: 55 pages, 7 figures, typos corrected, references added, version to
appear in Phys. Rev.

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