2,407 research outputs found
Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
Entanglement entropies calculated in the framework of quantum field theory on
classical, flat or curved, spacetimes are known to show an intriguing area law
in four dimensions, but they are also notorious for their quadratic ultraviolet
divergences. In this paper we demonstrate that the analogous entanglement
entropies when computed within the Asymptotic Safety approach to background
independent quantum gravity are perfectly free from such divergences. We argue
that the divergences are an artifact due to the over-idealization of a rigid,
classical spacetime geometry which is insensitive to the quantum dynamics.Comment: 19 page
Towards a -function in 4D quantum gravity
We develop a generally applicable method for constructing functions, ,
which have properties similar to Zamolodchikov's -function, and are
geometrically natural objects related to the theory space explored by
non-perturbative functional renormalization group (RG) equations. Employing the
Euclidean framework of the Effective Average Action (EAA), we propose a
-function which can be defined for arbitrary systems of gravitational,
Yang-Mills, ghost, and bosonic matter fields, and in any number of spacetime
dimensions. It becomes stationary both at critical points and in classical
regimes, and decreases monotonically along RG trajectories provided the
breaking of the split-symmetry which relates background and quantum fields is
sufficiently weak. Within the Asymptotic Safety approach we test the proposal
for Quantum Einstein Gravity in dimensions, performing detailed numerical
investigations in . We find that the bi-metric Einstein-Hilbert truncation
of theory space introduced recently is general enough to yield perfect
monotonicity along the RG trajectories, while its more familiar single-metric
analog fails to achieve this behavior which we expect on general grounds.
Investigating generalized crossover trajectories connecting a fixed point in
the ultraviolet to a classical regime with positive cosmological constant in
the infrared, the -function is shown to depend on the choice of the
gravitational instanton which constitutes the background spacetime. For de
Sitter space in 4 dimensions, the Bekenstein-Hawking entropy is found to play a
role analogous to the central charge in conformal field theory. We also comment
on the idea of a `- connection' and the `-bound' discussed
earlier.Comment: 15 figures; additional comment
Propagating gravitons vs. dark matter in asymptotically safe quantum gravity
Within the Asymptotic Safety scenario, we discuss whether Quantum Einstein
Gravity (QEG) can give rise to a semi-classical regime of propagating physical
gravitons (gravitational waves) governed by an effective theory which complies
with the standard rules of local quantum field theory. According to earlier
investigations based on single-metric truncations there is a tension between
this requirement and the condition of Asymptotic Safety since the former
(latter) requires a positive (negative) anomalous dimension of Newton's
constant. We show that the problem disappears using the bi-metric
renormalization group flows that became available recently: They admit an
asymptotically safe UV limit and, at the same time, a genuine semi-classical
regime with a positive anomalous dimension. This brings the gravitons of QEG on
a par with arbitrary (standard model, etc.) particles which exist as asymptotic
states. We also argue that metric perturbations on almost Planckian scales
might not be propagating, and we propose an interpretation as a form of `dark
matter'.Comment: 12 figures; further discussions adde
The unitary conformal field theory behind 2D Asymptotic Safety
Being interested in the compatibility of Asymptotic Safety with Hilbert space
positivity (unitarity), we consider a local truncation of the functional RG
flow which describes quantum gravity in dimensions and construct its
limit of exactly two dimensions. We find that in this limit the flow displays a
nontrivial fixed point whose effective average action is a non-local functional
of the metric. Its pure gravity sector is shown to correspond to a unitary
conformal field theory with positive central charge . Representing the
fixed point CFT by a Liouville theory in the conformal gauge, we investigate
its general properties and their implications for the Asymptotic Safety
program. In particular, we discuss its field parametrization dependence and
argue that there might exist more than one universality class of metric gravity
theories in two dimensions. Furthermore, studying the gravitational dressing in
2D asymptotically safe gravity coupled to conformal matter we uncover a
mechanism which leads to a complete quenching of the a priori expected
Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this
prediction to Monte Carlo results obtained in the discrete approach to 2D
quantum gravity based upon causal dynamical triangulations is mentioned.
Similarities of the fixed point theory to, and differences from, non-critical
string theory are also described. On the technical side, we provide a detailed
analysis of an intriguing connection between the Einstein-Hilbert action in
dimensions and Polyakov's induced gravity action in two dimensions.Comment: 64 page
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