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Marc Schiffer

Publications and source records attributed to Marc Schiffer.

At least 19 recordsLinked to original sources
arXiv2025

Yukawa interactions in Quantum Gravity

We present the first complete next-to-leading-order analysis of a Yukawa system within the framework of asymptotically safe quantum gravity. Our results are obtained through a systematic resummation of higher-order operators, revealing two distinct resummation mechanisms -- one of which has not been explored previously. In addition, we introduce a novel approach to estimate systematic uncertainties by simulating the impact of neglected higher-order contributions. We demonstrate that quantum gravity fluctuations anti-screen Yukawa interactions, thereby resolving previously inconclusive leading-order results. This anti-screening mechanism enables the generation of finite interactions from an asymptotically free Yukawa fixed point. Consequently, our findings provide strong evidence that non-vanishing Yukawa couplings are compatible with asymptotically safe quantum gravity, which is a necessary requirement for the Standard Model to emerge from an asymptotically safe ultraviolet completion.

hep-th↗
arXiv2025

Asymptotically safe quantum gravity: functional and lattice perspectives

Asymptotically safe quantum gravity is a candidate theory to quantum gravity, which could unify the gravitational interaction with particle physics. It is characterized by quantum scale-symmetry at high energies. The constraining power of scale symmetry could be strong enough to even explain some parameters of the Standard Model of particle physics from first principles.

gr-qc↗
arXiv2025

Non-Perturbative $S$-matrix Renormalization

We propose a renormalization group flow equation for a functional that generates $S$-matrix elements and which captures similarities to the well-known Wetterich and Polchinski equations. While the latter ones respectively involve the effective action and Schwinger functional, which are genuine off-shell objects, the presented flow equation has the advantage of working more directly with observables, i.e. scattering amplitudes. Compared to the Wetterich equation, our flow equation also greatly simplifies the notion of going on-shell, in the sense of satisfying the quantum equations of motion. In addition, unlike the Wetterich equation, it is polynomial and does not require a Hessian inversion. The approach is a promising direction for non-perturbative quantum field theories, allowing one to work more directly with scattering amplitudes.

hep-th↗
arXiv2025

Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity

Both General Relativity and the Standard Model of particle physics are not UV complete. General Relativity is perturbatively non-renormalizable, while the Standard Model features Landau poles, where couplings are predicted to diverge at finite energies, e.g., in the Abelian gauge sector. Asymptotically safe quantum gravity may resolve both of these issues at the same time. In this paper, we assess the systematic uncertainties associated with this scenario, in particular with the gravitationally induced UV-completion of the Abelian gauge sector. Specifically, we study the dependence of this qualitative feature, namely the existence of a UV-complete gauge sector, on unphysical choices like the gauge, and the regulator function. Intriguingly, in some scenarios, we find simultaneous points of minimal sensitivity relative to both the regulator and gauge parameters, which allow for a UV completion. This provides further indications that the simultaneous UV-completion of quantum gravity and matter via an asymptotically safe fixed point is a robust physical feature, and that physical quantities, like scaling exponents, can become independent of unphysical choices.

hep-th↗
arXiv2025

Renormalization group flows in area-metric gravity

We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as additional shape-mismatching degrees of freedom. To be phenomenologically viable, the shape-mismatching degrees of freedom have to decouple under the renormalization group flow towards lower scales. We test this scenario by calculating the renormalization group flow of the masses and find that these are in general even more relevant than dictated by their canonical scaling dimension. This generically results in masses which are large compared to the Planck mass and thereby ensure the decoupling of shape-mismatching degrees of freedom. In addition, the latter come in a left-handed and right-handed sector. We find that parity symmetry does not emerge under the renormalization group flow. Finally, we extract the renormalization group flow of the Immirzi parameter from this setup and find that its beta function features zeros at vanishing as well as at infinite Immirzi parameter.

gr-qc↗
arXiv2025

Indications against dynamical CPT symmetry restoration in quantum gravity

CPT symmetry is at the heart of the Standard Model of particle physics and experimentally very well tested, but expected to be broken in some approaches to quantum gravity. It thus becomes pertinent to explore which of the two alternatives is realized: (i) CPT symmetry is emergent, so that it is restored in the low-energy theory, even if it is broken beyond the Planck scale, (ii) CPT symmetry cannot be emergent and must be fundamental, so that any approach to quantum gravity, in which CPT is broken, is ruled out. We explore this by calculating the Renormalization Group flow of CPT violating interactions under the impact of quantum fluctuations of the metric. We find that CPT symmetry cannot be emergent and conclude that quantum-gravity approaches must avoid the breaking of CPT symmetry. As a specific example, we discover that in asymptotically safe quantum gravity CPT symmetry remains intact, if it is imposed as a fundamental symmetry, but it is badly broken at low energies if a tiny amount of CPT violation is present in the transplanckian regime.

gr-qc↗
arXiv2025

Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment

We provide a conceptual assessment of some aspects of fundamental quantum field theories of gravity in light of foundational aspects of the swampland program. On the one hand, asymptotically safe quantum gravity may provide a simple and predictive framework, thanks to a finite number of relevant parameters. On the other hand, a (sub-)set of intertwined swampland conjectures on the consistency of quantum gravity can be argued to be universal via effective field theory considerations. We answer whether some foundational features of these frameworks are compatible. This involves revisiting and refining several arguments (and loopholes) concerning the relation between field-theoretic descriptions of gravity and general swampland ideas. We identify the thermodynamics of black holes, spacetime topology change, and holography as the core aspects of this relation. We draw lessons on the features that a field theoretic description of gravity must (not) have to be consistent with fundamental principles underlying the swampland program, and on the universality of the latter.

hep-th↗
arXiv2024

Dynamical Dark Energy from Lattice Quantum Gravity

We study the behavior of the vacuum in Euclidean dynamical triangulations (EDT). Algorithmic improvements and better lattice spacing determinations allow us to test the properties of the emergent de Sitter geometries of our simulations to higher precision than previously possible. Although the agreement with de Sitter is good, the improved precision reveals deviations that can be interpreted as non-trivial vacuum dynamics, well-described by a cosmological constant that runs with scale. The simulations show that the dominant running is quadratic and that the scale can be identified with the Hubble rate. Several key cross-checks support this picture, including consistent results across multiple lattice spacings and the fact that the null energy condition is not violated. The parameters of the running are fully determined by simulations, enabling predictions when extrapolated to the scales relevant for our universe. This leads to a model for dark energy that is compatible with current observations, but which predicts deviations from $\Lambda$CDM at the ${\cal O}(10^{-3})$ level in cosmological observables that could be tested with future improvements in precision measurements.

hep-lat↗
arXiv2024

Spikes and spines in 4D Lorentzian simplicial quantum gravity

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for such configurations. They pose a significant challenge for a desired continuum limit, for which the average lengths of edges ought to become very small. Here we investigate spike and spine configurations in four-dimensional Lorentzian quantum Regge calculus. We find that the expectation values of arbitrary powers of the bulk length are finite. To that end, we explore new types of asymptotic regimes for the Regge amplitudes, in which some of the edges are much larger than the remaining ones. The amplitudes simplify considerably in such asymptotic regimes and the geometric interpretation of the resulting expressions involves a dimensional reduction, which might have applications to holography.

gr-qc↗
arXiv2024

Spikes and spines in 3D Lorentzian simplicial quantum gravity

Simplicial approaches to quantum gravity such as Quantum Regge Calculus and Spin Foams include configurations where bulk edges can become arbitrarily large while keeping the lengths of the boundary edges small. Such configurations pose significant challenges in Euclidean Quantum Regge Calculus, as they lead to infinities for the partition function and length expectation values. Here we investigate such configurations in three-dimensional Lorentzian Quantum Regge Calculus, and find that the partition function and length expectation values remain finite. This shows that the Lorentzian approach can avoid a key issue of the Euclidean approach. We also find that the space of configurations, for which bulk edges can become very large, is much richer than in the Euclidean case. In particular, it includes configurations with irregular light-cone structures, which lead to imaginary terms in the Regge action and branch cuts along the Lorentzian path integral contour. Hence, to meaningfully define the Lorentzian Regge path integral, one needs to clarify how such configurations should be handled.

gr-qc↗
arXiv2024

Application of positivity bounds in asymptotically safe gravity

Positivity bounds are bounds on the Wilson coefficients of an effective field theory. They hold, if the ultraviolet completion satisfies unitarity, microcausality, locality and Lorentz symmetry; accordingly their violation signals a violation of at least one of these properties of the ultraviolet completion. We explore whether positivity bounds on four-photon-couplings hold, when the ultraviolet completion is an asymptotically safe gravity-photon theory. By working at sixth order in an expansion in the electromagnetic field strength, we discover indications that positivity bounds hold for effective field theories that are UV completed by the asymptotically safe Reuter fixed point. We also perform various tests of the robustness of our result. This amounts to a nontrivial and critical indication of the physical viability of asymptotically safe gravity.

hep-th↗
arXiv2023

An improved algorithm for dynamical triangulations and simulations of finer lattices

We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of local and global terms in the action, a condition needed for efficient simulation of theories with global terms, while still maintaining detailed balance. We test our algorithm on the $2d$ Ising model, and against results for EDT obtained with standard Metropolis. Our new algorithm allows us to simulate EDT at finer lattice spacings than previously possible, and we find geometries that resemble semiclassical Euclidean de Sitter space in agreement with earlier results at coarser lattices. The agreement between lattice data and the classical de Sitter solution continues to get better as the lattice spacing decreases.

hep-lat↗
arXiv2023

On the weak-gravity bound for a shift-symmetric scalar field

The weak-gravity bound has been discovered in several asymptotically safe gravity-matter systems. It limits the strength of gravitational fluctuations that are compatible with an ultraviolet-complete matter sector, and results from the collision of two partial fixed points of the matter system as a function of the strength of the gravitational interactions. In this paper, we will investigate this mechanism in detail for a shift-symmetric scalar field. First, we will study the fixed point structure of the scalar system without gravity. We find indications that the Gaussian fixed point is the only viable fixed point, suggesting that a weak-gravity bound resulting from the collision of two partial fixed points is a truncation artefact. We will then couple the scalar system to gravity and perform different expansions to track the Gaussian fixed point as gravitational fluctuations become stronger. We also introduce a new notion of the weak-gravity bound that is based on the number of relevant operators.

hep-th↗
arXiv2022

Asymptotic safety of gravity with matter

The asymptotic-safety paradigm posits that the symmetry of quantum theories of gravity and matter is enhanced to quantum scale symmetry, i.e., scale symmetry in the presence of quantum fluctuations, at very high energies. To achieve such a symmetry enhancement, the effect of quantum fluctuations must balance out. It is to be expected that such a balance can only be achieved within a set of theories with limited field content and interaction structure. In this chapter, we review how much is known about these limits. From the quantum scale invariant regime, the theory transits to a theory with distinct physical scales - most importantly masses for various elementary particles - at low energies. There, quantum scale invariance can leave its imprint in relations between various interactions and mass scales of the theory. These relations can be compared to experimental data, which has two possible implications: first, if the relations do not match the data, the underlying quantum theory of gravity and matter, formulated at and beyond the Planck scale, has been ruled out using experimental data from energies much below the Planck scale. Second, if the relations match the data, the asymptotic-safety paradigm provides a first-principles derivation of free parameters of the Standard Model. Most importantly, this may include the ratios of the Higgs mass to the electroweak scale as well as the value of the finestructure constant. Similarly, theories beyond the Standard Model may come with fewer free parameters than in their effective-field-theory incarnation without gravity. This may lead to an explanation of the smallness of neutrinos masses and predictions for the nature and interactions of dark matter.

hep-th↗
arXiv2022

Configuration space for quantum gravity in a locally regularized path integral

We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parameterization of Euclidean metric fluctuations such that i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and ii) the parameterization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parameterize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a non-perturbative renormalization group setup.

hep-th↗
arXiv2021

The weak-gravity bound in asymptotically safe gravity-gauge systems

The weak-gravity bound has been discovered in asymptotically safe gravity-matter systems, where it limits the maximum strength of gravitational fluctuations. In the present paper, we explore it for the first time in systems with more than one gauge field, to discover whether systems with 12 gauge fields (like the Standard Model) exhibit a weak-gravity bound and whether the gravitational fixed point evades it. Further, we test the robustness of the present and previous results on the weak-gravity bound by exploring their dependence on a gravitational gauge parameter. Finally, the existence of the weak-gravity bound also has important phenomenological consequences: it is key to a proposed mechanism that bounds the spacetime dimensionality from above to four or five dimensions. In this paper, we strengthen the evidence for this mechanism. Thus, the predictive power of the asymptotic safety paradigm could extend to parameters of the spacetime geometry, such that the four-dimensionality of our universe could be explained from first principles.

gr-qc↗
arXiv2021

Light charged fermions in quantum gravity

We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions.

hep-th↗