There exist several distinct phenomenological models to generate neutrino masses. We explore which of these models can consistently be embedded in a quantum theory of gravity and matter. We proceed by invoking a minimal number of degrees of freedom beyond the Standard Model. Thus, we first investigate whether the Weinberg operator, a dimension-five operator that generates neutrino masses without requiring degrees of freedom beyond the Standard Model, can arise in asymptotically safe quantum gravity. We find a negative answer with far-reaching consequences: new degrees of freedom beyond gravity and the Standard Model are necessary to give neutrinos a mass in the asymptotic-safety paradigm. Second, we explore whether the type-I seesaw mechanism is viable and discover an upper bound on the seesaw scale. The bound depends on the mass of the visible neutrino. We find a numerical value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mn>10</mn><mn>14</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> for this bound when neglecting neutrino mixing for a visible mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Conversely, for the most “natural” value of the seesaw scale in a quantum-gravity setting, which is the Planck scale, we predict an upper bound for the neutrino mass of the visible neutrino of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mn>10</mn><mrow><mo>−</mo><mn>15</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Third, we explore whether neutrinos could also be pseudo-Dirac neutrinos in asymptotic safety and find that this possibility can be accommodated.

Brazil

Gustavo P. de Brito

Germany

Astrid Eichhorn

Antonio D. Pereira

Japan

Masatoshi Yamada

Neutrino mass generation in asymptotically safe gravity

We investigate whether quantum gravity fluctuations can break chiral symmetry for fermions that are charged under a U(1) and an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><msub><mrow><mi>N</mi></mrow><mi mathvariant="normal">c</mi></msub><mo stretchy="false">)</mo></mrow></math> gauge symmetry and thus closely resemble Standard-Model fermions. Unbroken chiral symmetry in the quantum-gravity regime is a necessary prerequisite to recover the Standard Model from a joint gravity-matter theory; if chiral symmetry is broken by quantum gravity, fermions cannot generically be much lighter than the Planck mass, and the theory is ruled out. To answer this, we work in a Fierz-complete basis of four-fermion interactions and explore whether they are driven to criticality. We discover that the interplay of quantum gravity with the non-Abelian gauge theory results in chiral symmetry breaking, because gravitational and gauge field fluctuations act together to produce bound states. Chiral symmetry breaking is triggered by four-fermion channels that first appear when non-Abelian charges are introduced and that become critical if the non-Abelian symmetry is gauged. Extrapolating our result to the Standard Model fermions, we conjecture that the non-Abelian gauge coupling, Abelian gauge coupling and Newton coupling are all bounded from above at trans-Planckian scales, if Standard Model fermions are to remain much lighter than the Planck mass. In contrast, fermions that are charged under a global non-Abelian group can remain light for arbitrarily large values of the Newton coupling. We find that different chiral symmetries are emergent at low energies, depending on the strength of the gravitational coupling. This is an example of fixed points with different degrees of enhanced global symmetry trading stability in fixed-point collisions driven by gravitational fluctuations.

Denmark

Faroe Islands

Shouryya Ray

Why the quark mass is not the Planck mass

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.

Canada

Marc Schiffer

Andreas Pedersen

Application of positivity bounds in asymptotically safe gravity

Combining asymptotically safe quantum gravity with a tensor field theory, we exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a nonvanishing value of the scalar quartic coupling. We first present (further) evidence that in the asymptotic-safety paradigm, quantum fluctuations of gravity generically screen the quartic couplings in (multi)scalar models. For a tensor field theory in which the scalar field transforms under an internal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><msup><mo stretchy="false">)</mo><mn>3</mn></msup></math> symmetry, this has the effect of replacing asymptotic freedom, recently discovered at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> on a fixed flat background, by an interacting fixed point in the presence of quantum gravity. The fixed point originates from the competition between the effects of the matter self-interactions which, contrary to the usual scalar models, are antiscreening, and the screening gravitational effects.

Razvan Gurau

Zois Gyftopoulos

Asymptotic safety meets tensor field theory: Toward a new class of gravity-matter systems

The nature of dark matter is a problem with too many potential solutions. We investigate whether a consistent embedding into quantum gravity can decimate the number of solutions to the dark-matter problem. Concretely, we focus on a hidden sector composed of a gauge field and a charged scalar, with gauge group <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>D</mi></msub></mrow></math> or <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mi>D</mi></msub></mrow></math>. The gauge field is the dark matter candidate, if the gauge symmetry is broken spontaneously. Phenomenological constraints on the couplings in this model arise from requiring that the correct dark matter relic density is produced via thermal freeze-out and that recent bounds from direct-detection experiments are respected. We find that the consistent embedding into asymptotically safe quantum gravity gives rise to additional constraints on the couplings at the Planck scale, from which we calculate corresponding constraints at low energy scales. We discover that phenomenological constraints cannot be satisfied simultaneously with theoretical constraints from asymptotically safe quantum gravity, ruling out these dark matter models.

Mads T. Frandsen

United Kingdom

Martin Rosenlyst

Mattias E. Thing

Arthur F. Vieira

Ruling out models of vector dark matter in asymptotically safe quantum gravity

The bound on the proton lifetime is one of a small handful of observations that constrains physics not far from the Planck scale. This calls for a calculation of the proton lifetime in quantum gravity. Here, we calculate how quantum fluctuations of the metric impact four-fermion interactions which mediate proton decay. We find that quantum gravity lowers the scaling dimension of the four-fermion interaction, suppressing proton decay and raising the proton lifetime significantly.As a special case, we analyze asymptotically safe quantum gravity, in which we discover that proton-decay-mediating four-fermion interactions are strictly zero.

Suppression of proton decay in quantum gravity

We present a mechanism which drives Dirac neutrino masses to tiny values along the Renormalization Group flow, starting from an asymptotically safe ultraviolet completion of the third generation of the Standard Model including quantum gravity. At the same time, the mechanism produces a mass-splitting between the neutrino and the quark sector and also generates the mass splitting between top and bottom quark. The mechanism hinges on the hypercharges of the fermions and produces a tiny neutrino Yukawa coupling, because the right-handed neutrino is sterile and does not carry hypercharge.

United States

Aaron Held

Dynamically vanishing Dirac neutrino mass from quantum scale symmetry

We explore the effect of quantum gravity on matter within a Renormalization Group framework. First, our results provide an explicit example of how misleading conclusions can be drawn by analyzing the gravitational contributions to beta functions, instead of analyzing universal quantities, such as critical exponents, that can be extracted from the beta functions. This could be key to explain differences between perturbative studies and Functional Renormalization Group studies. Second, we strengthen the evidence that asymptotically safe gravity could generate a predictive ultraviolet completion for matter theories with gauge interactions, even in the limit of vanishing dimensionful regulator function. We also find that the situation can be more subtle with higher-order, gravity-induced matter interactions.

Gustavo Brito

Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators

We investigate axion-like particles (ALPs) in the context of asymptotically safe gravity-matter systems. The ALP-photon interaction, which facilitates experimental searches for ALPs, is a dimension-5-operator. Quantum fluctuations of gravity lower its scaling dimension, and the ALP-photon coupling can become asymptotically free or even asymptotically safe. However, quantum fluctuations of gravity need to be strong to overcome the canonical scaling and this strong-gravity regime is in tension with the weak-gravity bound in asymptotic safety. Thus, we tentatively conclude that fundamental ALPs can likely not be accommodated in asymptotically safe gravity-matter systems. In turn, an experimental discovery of an ALP would thus shed valuable light on the quantum nature of gravity.

Rafael Lino dos Santos

Are there ALPs in the asymptotically safe landscape?

We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this critical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.