arXiv subjects

Holger Gies

Publications and source records attributed to Holger Gies.

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↗

arXiv2019

Propagator from Nonperturbative Worldline Dynamics

We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling in the quenched limit (small-$N_{\text{f}}$ expansion). Specifically, we consider a simple two-scalar field theory with cubic interaction (S${}^2$QED) in four dimensions as a toy model for QED-like theories. Using a worldline regularization technique, we are able to analyze the divergence structure of all-order diagrams and to perform the renormalization of the model nonperturbatively. Our method gives us access to a wide range of couplings and coordinate distances. We compute the pole mass of the S${}^2$QED electron and observe sizable nonperturbative effects in the strong-coupling regime arising from the full photon dressing. We also find indications for the existence of a critical coupling where the photon dressing compensates the bare mass such that the electron mass vanishes. The short distance behavior remains unaffected by the photon dressing in accordance with the power-counting structure of the model.

hep-th↗

arXiv2019

Momentum dependence of quantum critical Dirac systems

We analyze fermionic criticality in relativistic 2+1 dimensional fermion systems using the functional renormalization group (FRG), concentrating on the Gross-Neveu (chiral Ising) and the Thirring model. While a variety of methods, including the FRG, appear to reach quantitative consensus for the critical regime of the Gross-Neveu model, the situation seems more diverse for the Thirring model with different methods yielding vastly different results. We present a first exploratory FRG study of such fermion systems including momentum-dependent couplings using pseudo-spectral methods. Our results corroborate the stability of results in Gross-Neveu-type universality classes, but indicate that momentum dependencies become more important in Thirring-type models for small flavor numbers. For larger flavor numbers, we confirm the existence of a non-Gaussian fixed point and thus a physical continuum limit. In the large-$N$ limit, we obtain an analytic solution for the momentum dependence of the fixed-point vertex.

hep-th↗

arXiv2019

Scheme dependence of asymptotically free solutions

Recent studies have provided evidence for the existence of new asymptotically free trajectories in non-Abelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general ${\rm SU}(N_{\rm L})\times {\rm SU}(N_{\rm c})$ Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies. We construct these asymptotically free trajectories within conventional $\overline{\text{MS}}$ schemes and systematic weak coupling expansions. The existence of these solutions is argued to be a scheme-independent phenomenon, as demonstrated for mass-dependent schemes based on general momentum-space infrared regularizations. A change of scheme induces a map of the theory's coupling space onto itself, which in the present case also translates into a reparametrization of the space of asymptotically free solutions.

hep-th↗

arXiv2018

The Vacuum Emission Picture Beyond Paraxial Approximation

Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent electromagnetic fields. Recent studies have adopted this approach to study collisions of Gaussian laser pulses in paraxial approximation. The present study extends these investigations beyond the paraxial approximation by using an efficient numerical solver for the classical input fields. This new numerical code allows for a consistent theoretical description of optical signatures of QED vacuum nonlinearities in generic electromagnetic fields governed by Maxwell's equations in the vacuum, such as manifestly non-paraxial laser pulses. Our code is based on a locally constant field approximation of the Heisenberg-Euler effective Lagrangian. As this approximation is applicable for essentially all optical high-intensity laser experiments, our code is capable of calculating signal photon emission amplitudes in completely generic input field configurations, limited only by numerical cost.

physics.optics↗

arXiv2018

Photon-Photon Scattering at the High-Intensity Frontier: Paraxial Beams

Our goal is to study optical signatures of quantum vacuum nonlinearities in strong macroscopic electromagnetic fields provided by high-intensity laser beams. The vacuum emission scheme is perfectly suited for this task as it naturally distinguishes between incident laser beams, described as classical electromagnetic fields driving the effect, and emitted signal photons encoding the signature of quantum vacuum nonlinearity. Using the Heisenberg-Euler effective action, our approach allows for a reliable study of photonic signatures of QED vacuum nonlinearity in the parameter regimes accessible by all-optical high-intensity laser experiments. To this end, we employ an efficient, flexible numerical algorithm, which allows for a detailed study of the signal photons emerging in the collision of focused paraxial high-intensity laser pulses. Due to the high accuracy of our numerical solutions we predict the total number of signal photons, but also have full access to the signal photons' characteristics, including their spectrum, propagation directions and polarizations. We discuss setups offering an excellent background-to-noise ratio, thus providing an important step towards the experimental verification of quantum vacuum nonlinearities.

hep-ph↗

arXiv2018

All-optical signatures of quantum vacuum nonlinearities in generic laser fields

All-optical experiments at the high-intensity frontier offer a promising route to unprecedented precision tests of quantum electrodynamics in strong macroscopic electromagnetic fields. So far, most theoretical studies of all-optical signatures of quantum vacuum nonlinearity are based on simplifying approximations of the beam profiles and pulse shapes of the driving laser fields. Since precision tests require accurate quantitative theoretical predictions, we introduce an efficient numerical tool facilitating the quantitative theoretical study of all-optical signatures of quantum vacuum nonlinearity in generic laser fields. Our approach is based on the vacuum emission picture, and makes use of the fact that the dynamics of the driving laser fields are to an excellent approximation governed by classical Maxwell theory in vacuum. In combination with a Maxwell solver, which self-consistently propagates any given laser field configuration, this allows for accurate theoretical predictions of photonic signatures of vacuum nonlinearity in high-intensity laser experiments from first principles. We employ our method to simulate photonic signatures of quantum vacuum nonlinearity in laser pulse collisions involving a few-cycle pulse, and show that the angular and spectral distributions of the emitted signal photons deviate from those of the driving laser beams.

physics.optics↗

arXiv2018

BRST invariant RG flows

A mass parameter for the gauge bosons in gauge-fixed four-dimensional Yang-Mills theory can be accommodated in a local and manifestly BRST-invariant action. The construction is based on the Faddeev-Popov method involving a nonlinear gauge-fixing and a background Nakanishi-Lautrup field. When applied to momentum-dependent masslike deformations, this formalism leads to a full regularization of the theory which explicitly preserves BRST symmetry. We deduce a functional renormalization group equation for the one-particle-irreducible effective action, which has a one-loop form. The master equation is compatible with it, i.e. BRST symmetry is preserved along the flow, and it has a standard regulator-independent Zinn-Justin form. As a first application, we compute the leading-order gluon wave-function renormalization.

hep-th↗

arXiv2018

Asymptotic freedom in ${Z}_2$-Yukawa-QCD models

${Z}_2$-Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.

hep-th↗

arXiv2018

Probing Baryogenesis through the Higgs Self-Coupling

The link between a modified Higgs self-coupling and the strong first-order phase transition necessary for baryogenesis is well explored for polynomial extensions of the Higgs potential. We broaden this argument beyond leading polynomial expansions of the Higgs potential to higher polynomial terms and to non-polynomial Higgs potentials. For our quantitative analysis we resort to the functional renormalization group, which allows us to evolve the full Higgs potential to higher scales and finite temperature. In all cases we find that a strong first-order phase transition manifests itself in an enhancement of the Higgs self-coupling by at least 50%, implying that such modified Higgs potentials should be accessible at the LHC.

hep-ph↗

arXiv2018

Photon-photon scattering at the high-intensity frontier

The tremendous progress in high-intensity laser technology and the establishment of dedicated high-field laboratories in recent years have paved the way towards a first observation of quantum vacuum nonlinearities at the high-intensity frontier. We advocate a particularly prospective scenario, where three synchronized high-intensity laser pulses are brought into collision, giving rise to signal photons, whose frequency and propagation direction differ from the driving laser pulses, thus providing various means to achieve an excellent signal to background separation. Based on the theoretical concept of vacuum emission, we employ an efficient numerical algorithm which allows us to model the collision of focused high-intensity laser pulses in unprecedented detail. We provide accurate predictions for the numbers of signal photons accessible in experiment. Our study paves the way for a first verification of quantum vacuum nonlinearity in a well-controlled laboratory experiment at one of the many high-intensity laser facilities currently coming online.

hep-ph↗

arXiv2018

A curvature bound from gravitational catalysis

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.

hep-th↗

arXiv2018

A functional perspective on emergent supersymmetry

We investigate the emergence of ${\cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the $ε$-expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.

hep-th↗

arXiv2017

All-optical signatures of Strong-Field QED in the vacuum emission picture

We study all-optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum, using the collision of two focused high-intensity laser pulses as an example. The experimental signatures of quantum vacuum nonlinearities are encoded in signal photons, whose kinematic and polarization properties differ from the photons constituting the macroscopic laser fields. We implement an efficient numerical algorithm allowing for the theoretical investigation of such signatures in realistic field configurations accessible in experiment. This algorithm is based on a vacuum emission scheme and can readily be adapted to the collision of more laser beams or further involved field configurations. We solve the case of two colliding pulses in full 3+1 dimensional spacetime, and identify experimental geometries and parameter regimes with improved signal-to-noise ratios.

hep-ph↗

arXiv2017

Renormalization Group Flow of the Higgs Potential

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows to describe the effective potential as a function of both scalar field amplitude and RG scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.

hep-ph↗

arXiv2017

Impact of generalized Yukawa interactions on the lower Higgs mass bound

We investigate the impact of operators of higher canonical dimension on the lower Higgs mass consistency bound by means of generalized Higgs-Yukawa interactions. Analogously to higher-order operators in the bare Higgs potential in an effective field theory approach, the inclusion of higher-order Yukawa interactions, e.g., $ϕ^3\barψψ$, leads to a diminishing of the lower Higgs mass bound and thus to a shift of the scale of new physics towards larger scales by a few orders of magnitude without introducing a metastability in the effective Higgs potential. We observe that similar renormalization group mechanisms near the weak-coupling fixed point are at work in both generalizations of the microscopic action. Thus, a combination of higher-dimensional operators with generalized Higgs as well as Yukawa interactions does not lead to an additive shift of the lower mass bound, but relaxes the consistency bounds found recently only slightly. On the method side, we clarify the convergence properties of different projection and expansion schemes for the Yukawa potential used in the functional renormalization group literature so far.

hep-ph↗

arXiv2017

Critical Schwinger pair production II - universality in the deeply critical regime

We study electron-positron pair production by spatially inhomogeneous electric fields. Depending on the localization of the field, a critical point (critical surface) exists in the space of field configurations where the pair production probability vanishes. Near criticality, pair production exhibits universal properties similar to those of continuous phase transitions. We extend results previously obtained in the semi-classical (weak-field) critical regime to the deeply critical regime for arbitrary peak field strength. In this regime, we find an enhanced universality, featuring a unique critical exponent $β=3$ for all sufficiently localized fields. For a large class of field profiles, we also compute the non-universal amplitudes.

hep-th↗

arXiv2016

Nonabelian Higgs models: paving the way for asymptotic freedom

Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.

hep-ph↗