A formalism is presented for the treatment of space-times, which is intermediate between a fully covariant approach and the spin-coefficient method of Newman and Penrose. With the present formalism, a pair of null directions only, rather than an entire null tetrad, is singled out at each point. The concept of a spin- and boost-weighted quantity is defined, the formalism operating entirely with such quantities. This entails the introduction of modified differentiation operators, one of which represents a natural extension of the definition of the operator ð which had been introduced earlier by Newman and Penrose. For suitable problems, the present formalism should lead to considerable simplifications over that achieved by the standard spin-coefficient method.

We highlight how the existence of an ultraviolet completion for interacting Standard-Model type matter puts constraints on the viable microscopic dynamics of asymptotically safe quantum gravity within truncated Renormalization Group flows. A first constraint -the weak-gravity bound -is rooted in the destruction of quantum scale-invariance in the matter system by strong quantumgravity fluctuations. A second constraint arises by linking Planck-scale dynamics to the dynamics at the electroweak scale. Specifically, we delineate how to extract a prediction of the top quark mass from asymptotically safe gravity and stress that a finite top mass could be difficult to accommodate in a significant part of the gravitational coupling space. I. CONNECTING QUANTUM GRAVITY TO THE ELECTROWEAK SCALEObservational guidance on the route to quantum gravity is notoriously elusive. For most "smoking-gun" signals of quantum gravity, the Planck scale would have to be accessible by controlled experiments, as effects are typically suppressed by the energy scale of the experiment over the Planck scale. Here, we discuss how to restrict the microscopic quantum-gravity dynamics by bridging the gap in the hierarchy of scales between Planck and electroweak scale in terms of a Wilsonian Renormalization Group (RG) flow. Recovering experimentally tested particle physics at the electroweak scale restricts the form of the microscopic dynamics including quantum gravity. In particular, the microscopic model could even be a fundamental quantum field theory of gravity and matter within the asymptotic-safety paradigm [1]. That scenario generalizes the success-story of asymptotic freedom -where a free RG fixed point underlies quantum scale-invariance in the ultraviolet (UV) -to an interacting UV complete theory. Based on the groundbreaking work of Reuter [2], compelling hints for asymptotic safety in pure gravity have been found , see, e.g., [42] for reviews and [43,44] for possible consequences in astrophysics and cosmology. For asymptotically safe models without gravity see, e.g., [45][46][47][48].By including matter, we derive strong hints for two structurally different constraints on the gravitational coupling space: In the UV, we find a weak-gravity bound: A quantum-gravity induced fixed point for matter can only exist for sufficiently weak quantum-gravity fluctuations. Infrared (IR) physics at the electroweak scale imposes a second constraint on the UV fixed-point structure: We demand that an observationally viable dynamics arises along an RG trajectory emanating from the fixed point. Whenever quantum fluctuations of gravity generate a negative scaling dimension for a matter coupling, e.g., a Yukawa coupling, they force it to a specific value at the Planck scale. Assuming no new physics, its * a.eichhorn@thphys.uni-heidelberg.de † a.held@thphys.uni-heidelberg.de further RG flow is given by well-known Standard Model running down to the electroweak scale. This maps a microscopic fixed-point value to an IR quantity. The fixedpoint value depends on the...

A phenomenologically viable theory of quantum gravity must accommodate all observed matter degrees of freedom and their properties. Here, we explore whether a toy model of the Higgs-Yukawa sector of the Standard Model is compatible with asymptotically safe quantum gravity. We discuss the phenomenological implications of our result in the context of the Standard Model.We analyze the quantum scaling dimension of the system, and find an irrelevant Yukawa coupling at a joint gravity-matter fixed point. Further, we explore the impact of gravity-induced couplings between scalars and fermions, which are non-vanishing in asymptotically safe gravity.

We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately $170\, \rm GeV$ is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of $M_\text{t,pole} \approx 171\, \rm GeV$.Comment: Matches version accepted in Phys. Lett. B; counting of degrees of freedom in Eq.(7) changed, resulting in M_t=171 GeV and M_h=132 GeV; conclusions unchange

We propose a scenario to retrodict the top and bottom mass and the Abelian gauge coupling from first principles in a microscopic model including quantum gravity. In our approximation, antiscreening quantum-gravity fluctuations induce an asymptotically safe fixed point for the Abelian hypercharge leading to a uniquely fixed infrared value that is observationally viable for a particular choice of microscopic gravitational parameters. The unequal quantum numbers of the top and bottom quark lead to different fixed-point values for the top and bottom Yukawa under the impact of gauge and gravity fluctuations. This results in a dynamically generated mass difference between the two quarks. To work quantitatively, the preferred ratio of electric charges of bottom and top in our approximation lies in close vicinity to the Standard-Model value of Q b Qt = −1 2.