Searcharxiv⌕ Search

arXiv subjects

Roberto Percacci

Publications and source records attributed to Roberto Percacci.

At least 37 records · Page 2Linked to original sources
arXiv2020

Critical reflections on asymptotically safe gravity

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program.

gr-qc↗
arXiv2020

Quark masses and mixings in minimally parameterized UV completions of the Standard Model

We explore a simple parameterization of new physics that results in an ultraviolet complete gauge-quark sector of the Standard Model. Specifically, we add an antiscreening contribution to the beta functions of the gauge couplings and a flavor-independent, antiscreening contribution to the beta functions of the Yukawa couplings. These two free parameters give rise to an intricate web of Renormalization Group fixed points. Their predictive power extends to the flavor structure and mixing patterns, which we investigate to demonstrate that some of the free parameters of the Standard Model could be determined by the Renormalization Group flow.

hep-ph↗
arXiv2019

Trace anomaly and infrared cutoffs

The Effective Average Action is a form of effective action which depends on a cutoff scale suppressing the contribution of low momentum modes in the functional integral. It reduces to the ordinary effective action when the cutoff scale goes to zero. We derive the modifications of the scale Ward identity due to this cutoff and show how the resulting identity then intimately relates the trace anomaly to the Wilsonian realisation of the renormalization group.

hep-th↗
arXiv2019

Quantum fields without Wick rotation

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.

gr-qc↗
arXiv2018

Wicked metrics

There are various ways of defining the Wick rotation in a gravitational context. There are good arguments to view it as an analytic continuation of the metric, instead of the coordinates. We focus on one very general definition and argue that it is incompatible with the requirement of preserving the field equations and the symmetries at global level: in some cases the Euclidean metric cannot be defined on the original Lorentzian manifold but only on a submanifold. This phenomenon is related to the existence of horizons, as illustrated in the cases of the de Sitter and Schwarzschild metrics.

gr-qc↗
arXiv2018

Gravity with more or less gauging

General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation where it is only invariant under the smaller group of special diffeomorphisms. Other formulations with the same number of gauge generators, but a different gauge algebra, also exist. These different formulations provide examples of what we call 'inessential gauge invariance', 'symmetry trading' and 'linking theories'; they are locally equivalent, but may differ when global properties of the solutions are considered. We discuss these notions in the Lagrangian and Hamiltonian formalism.

gr-qc↗
arXiv2018

In search of a UV completion of the Standard Model - 378.000 models that don't work

Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and having Yukawa-like interactions with new scalar fields. Here we study the corresponding renormalization group beta functions to next and next-to-next to leading order in the perturbative expansion, varying the number of extra fermions and the representations they carry. We test the fixed points of the beta functions against various criteria of perturbativity to single out those that are potentially viable. We show that all the candidate ultraviolet fixed points are unphysical for these models: either they are unstable under radiative corrections, or they cannot be matched to the Standard Model at low energies.

hep-ph↗
arXiv2017

Gravity and Unification: A review

We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an "internal" space is enlarged. The starting point for each such unification scenario is a particular formalism for General Relativity. We thus start by reviewing, besides the usual Einstein-Hilbert and Palatini formulations, the Einstein-Cartan, MacDowell-Mansouri and BF (both non-chiral and chiral) formulations. Each of these introduces some version of "internal" bundle and a dynamical variable that ties the internal and tangent bundles. In each of these formulations there is also an independent connection in the "internal" bundle. One can then study the effects of "enlarging the internal space", which typically leads to a theory of gravity and Yang-Mills fields. We review what has been done in the literature on each of these unification schemes, and compare and contrast their achievements to those of the better developed Kaluza-Klein scenario.

hep-th↗
arXiv2017

Split Weyl transformations in quantum gravity

We discuss various realizations of the Weyl group in the background field expansion of quantum gravity, in the presence of a cutoff, as required in applications of the functional renormalization group. In order to study the background--dependence, special attention is given to split gauge transformations, which act on the background field and fluctuation keeping the total metric unchanged. The results generalize previous works on global and local scale transformations.

gr-qc↗
arXiv2017

The background scale Ward identity in quantum gravity

We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified flow equation that is manifestly invariant under global background rescalings.

hep-th↗
arXiv2016

Quantum gravity with torsion and non-metricity

We study the renormalization of theories of gravity with an arbitrary (torsionful and non-metric) connection. The class of actions we consider is of the Palatini type, including the most general terms with up to two derivatives of the metric, but no derivatives of the connection. It contains 19 independent parameters. We calculate the one loop beta functions of these parameters and find their fixed points. The Holst subspace is discussed in some detail and found not to be stable under renormalization. Some possible implications for ultraviolet and infrared gravity are discussed.

gr-qc↗
arXiv2016

Asymptotic safety in an interacting system of gravity and scalar matter

Asymptotic safety is an attractive scenario for the dynamics of quantum spacetime. Here, we work from a phenomenologically motivated point of view and emphasize that a viable dynamics for quantum gravity in our universe must account for the existence of matter. In particular, we explore the scale-dependence of a scalar matter-gravity-vertex, and investigate whether an interacting fixed point exists for the so-defined Newton coupling. We find a viable fixed point in the pure-gravity system, disregarding scalar quantum fluctuations. We explore its extensions to the case with dynamical scalars, and find indications of asymptotic safety in the matter-gravity system. We moreover examine the anomalous dimensions for different components of the metric fluctuations, and find significant differences between the transverse traceless and scalar component.

gr-qc↗
arXiv2016

Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization

We employ the exponential parametrization of the metric and a "physical" gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an $f(R)$ truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function $f$. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure.

hep-th↗
arXiv2015

Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories

We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful couplings different from linear split, though the fact that there exists nontrivial fixed point remains the same and the fixed points also remain the same.

hep-th↗
arXiv2015

A flow equation for f(R) gravity and some of its exact solutions

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the parameters the solution seems to be continuously deformed.

hep-th↗
arXiv2015

Asymptotic safety in $O(N)$ scalar models coupled to gravity

We extend recent results on scalar-tensor theories to the case of an O(N)-invariant multiplet. Some exact fixed point solutions of the RG flow equations are discussed. We find that also in the functional context, on employing a standard "type-I" cutoff, too many scalars destroy the gravitational fixed point. For d=3 we show the existence of the gravitationally dressed Wilson-Fisher fixed point also for N>1. We discuss also the results of the analysis for a different, scalar-free, coarse-graining scheme.

hep-th↗
arXiv2015

Computing the Effective Action with the Functional Renormalization Group

The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $Γ_k$. The ordinary effective action $Γ_0$ can be obtained by integrating the flow equation from an ultraviolet scale $k=Λ$ down to $k=0$. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We use the results of Barvinsky, Vilkovisky and Avramidi on the non-local heat kernel coefficients to reproduce the four point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.

hep-th↗