394 research outputs found
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 , supporting
space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 figure
Common Sense or World Knowledge? Investigating Adapter-Based Knowledge Injection into Pretrained Transformers
Following the major success of neural language models (LMs) such as BERT or
GPT-2 on a variety of language understanding tasks, recent work focused on
injecting (structured) knowledge from external resources into these models.
While on the one hand, joint pretraining (i.e., training from scratch, adding
objectives based on external knowledge to the primary LM objective) may be
prohibitively computationally expensive, post-hoc fine-tuning on external
knowledge, on the other hand, may lead to the catastrophic forgetting of
distributional knowledge. In this work, we investigate models for complementing
the distributional knowledge of BERT with conceptual knowledge from ConceptNet
and its corresponding Open Mind Common Sense (OMCS) corpus, respectively, using
adapter training. While overall results on the GLUE benchmark paint an
inconclusive picture, a deeper analysis reveals that our adapter-based models
substantially outperform BERT (up to 15-20 performance points) on inference
tasks that require the type of conceptual knowledge explicitly present in
ConceptNet and OMCS
The Renormalization Group, Systems of Units and the Hierarchy Problem
In the context of the Renormalization Group (RG) for gravity I discuss the
role of field rescalings and their relation to choices of units. I concentrate
on a simple Higgs model coupled to gravity, where natural choices of units can
be based on Newton's constant or on the Higgs mass. These quantities are not
invariant under the RG, and the ratio between the units is scale-dependent. In
the toy model, strong RG running occurs in the intermediate regime between the
Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I
model. Possible connections with the problem of the mass hierarchy are pointed
out.Comment: Plain TEX, 16 pages. Some revisions, some references adde
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 . 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 and 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 -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 -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.
Averaging procedure in variable-G cosmologies
Previous work in the literature had built a formalism for spatially averaged
equations for the scale factor, giving rise to an averaged Raychaudhuri
equation and averaged Hamiltonian constraint, which involve a backreaction
source term. The present paper extends these equations to include models with
variable Newton parameter and variable cosmological term, motivated by the
nonperturbative renormalization program for quantum gravity based upon the
Einstein-Hilbert action. We focus on the Brans-Dicke form of the
renormalization-group improved action functional. The coupling between
backreaction and spatially averaged three-dimensional scalar curvature is found
to survive, and a variable-G cosmic quintet is found to emerge. Interestingly,
under suitable assumptions, an approximate solution can be found where the
early universe tends to a FLRW model, while keeping track of the original
inhomogeneities through three effective fluids. The resulting qualitative
picture is that of a universe consisting of baryons only, while inhomogeneities
average out to give rise to the full dark-side phenomenology.Comment: 20 pages. In the new version, all original calculations have been
improved, and the presentation has been further improved as wel
Fractal Structure of Loop Quantum Gravity
In this paper we have calculated the spectral dimension of loop quantum
gravity (LQG) using simple arguments coming from the area spectrum at different
length scales. We have obtained that the spectral dimension of the spatial
section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar
field decrees from high to low energy. We have calculated the spectral
dimension of the space-time also using results from spin-foam models, obtaining
a 2-dimensional effective manifold at hight energy. Our result is consistent
with other two approach to non perturbative quantum gravity: causal dynamical
triangulation and asymptotic safety quantum gravity.Comment: 5 pages, 5 figure
Scale-dependent metric and causal structures in Quantum Einstein Gravity
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 average action of Quantum
Einstein Gravity (QEG) and the resulting families of resolution dependent
metrics are discussed. The status of scale dependent vs. scale independent
diffeomorphisms is clarified, and the difference between isometries implemented
by scale dependent and independent Killing vectors is explained. A concept of
scale dependent causality is proposed and illustrated by various simple
examples. The possibility of assigning an "intrinsic length" to objects in a
QEG spacetime is also discussed.Comment: 52 page
Fixed points of quantum gravity in extra dimensions
We study quantum gravity in more than four dimensions with renormalisation
group methods. We find a non-trivial ultraviolet fixed point in the
Einstein-Hilbert action. The fixed point connects with the perturbative
infrared domain through finite renormalisation group trajectories. We show that
our results for fixed points and related scaling exponents are stable. If this
picture persists at higher order, quantum gravity in the metric field is
asymptotically safe. We discuss signatures of the gravitational fixed point in
models with low-scale gravity and compact extra dimensions.Comment: Wording sharpened, refs added, to appear in PL
Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity
We review recent work on renormalization group (RG) improved cosmologies
based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic
parameter values. In particular we argue that QEG effects can account for the
entire entropy of the present Universe in the massless sector and give rise to
a phase of inflationary expansion. This phase is a pure quantum effect and
requires no classical inflaton field.Comment: 12 pages, 4 figures, IGCG-07 Pun
Critical exponents from optimised renormalisation group flows
Within the exact renormalisation group, the scaling solutions for O(N)
symmetric scalar field theories are studied to leading order in the derivative
expansion. The Gaussian fixed point is examined for d>2 dimensions and
arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is
studied using an optimised flow. We compute critical exponents and subleading
corrections-to-scaling to high accuracy from the eigenvalues of the stability
matrix at criticality for all N. We establish that the optimisation is
responsible for the rapid convergence of the flow and polynomial truncations
thereof. The scheme dependence of the leading critical exponent is analysed.
For all N > 0, it is found that the leading exponent is bounded. The upper
boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to
the large-N limit. The lower boundary is achieved by the optimised flow and is
closest to the physical value. We show the reliability of polynomial
approximations, even to low orders, if they are accompanied by an appropriate
choice for the regulator. Possible applications to other theories are outlined.Comment: 34 pages, 15 figures, revtex, to appear in NP
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