198 research outputs found
Lorentz symmetry is relevant
We set up a covariant renormalisation group equation on a foliated spacetime
which preserves background diffeomorphism symmetry. As a first application of
the new formalism, we study the effect of quantum fluctuations in Lorentz
symmetry breaking theories of quantum gravity. It is found that once a small
breaking is introduced e.g. at the Planck scale, quantum fluctuations enhance
this breaking at low energies. A numerical analysis shows that the
magnification is of order unity for trajectories compatible with a small
cosmological constant. The immediate consequence is that the stringent
observational constraints on Lorentz symmetry breaking are essentially
scale-independent and must be met even at the Planck scale.Comment: 10 pages, 1 figur
Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
We discuss the Heisenberg model and its chiral extension in an extended
truncation with the help of functional methods. Employing computer algebra to
derive the beta functions, and pseudo-spectral methods to solve them, we are
able to go significantly beyond earlier approximations, and provide new
estimates on the critical quantities of both models. The fixed point of the
Heisenberg model is mostly understood, and our results are in agreement with
estimates from various other approaches, including Monte Carlo and conformal
bootstrap studies. By contrast, in the chiral case, the formerly known
disagreement with lattice studies persists, raising the question whether
actually the same universality class is described.Comment: 10 pages, 5 figures; v2: matches journal versio
Towards reconstructing the quantum effective action of gravity
Starting from a parameterisation of the quantum effective action for gravity
we calculate correlation functions for observable quantities. The resulting
templates allow to reverse-engineer the couplings describing the effective
dynamics from the correlation functions. Applying this new formalism to the
autocorrelation function of spatial volume fluctuations measured within the
Causal Dynamical Triangulations program suggests that the corresponding quantum
effective action consists of the Einstein-Hilbert action supplemented by a
non-local interaction term. We expect that our matching-template formalism can
be adapted to a wide range of quantum gravity programs allowing to bridge the
gap between the fundamental formulation and observable low-energy physics.Comment: 6 pages, 1 figure; v2: reference update+clarification; v3: matches
published versio
Resolving Spacetime Singularities within Asymptotic Safety
A key incentive of quantum gravity is the removal of spacetime singularities
plaguing the classical theory. We compute the non-perturbative
momentum-dependence of a specific structure function within the gravitational
asymptotic safety program which encodes the quantum corrections to the graviton
propagator for momenta above the Planck scale. The resulting quantum corrected
Newtonian potential approaches a constant negative value as the distance
between the two point masses goes to zero, thereby removing the classical
singularity. The generic nature of the underlying mechanism suggests that it
will remain operative in the context of black hole and cosmic singularities.Comment: v2: some improvements and clarifications; version accepted for
publication in PR
Safe essential scalar-tensor theories
We discuss the renormalisation group flow of all essential couplings of
quantum gravity coupled to a shift-symmetric scalar field at fourth order in
the derivative expansion. We derive the global structure of the phase diagram,
and identify a bounded region in theory space which is both asymptotically safe
in the ultraviolet, and connects to standard effective field theory in the
infrared. Our system thus satisfies the weak-gravity bound. The allowed
infrared behaviour of the essential four-scalar coupling is restricted by
requiring an ultraviolet completion. This bound can be saturated by a theory
without free parameters, which gives a concrete example for a fully predictive
scalar-tensor theory.Comment: 25 pages, 1 ancillary Mathematica noteboo
Lessons from conformally reduced quantum gravity
In this work we study a significantly enlarged truncation of conformally
reduced quantum gravity in the context of Asymptotic Safety, including all
operators that can be resolved in such a truncation including up to the sixth
order in derivatives. A fixed point analysis suggests that there is no
asymptotically safe fixed point in this system once one goes beyond an
Einstein-Hilbert approximation. We will put these findings into context and
discuss some lessons that can be learned from these results for general
non-perturbative renormalisation group flows
- …