arXiv subjects

Astrid Eichhorn

Publications and source records attributed to Astrid Eichhorn.

At least 109 records · Page 6Linked to original sources

arXiv2018

Quantum gravity fluctuations flatten the Planck-scale Higgs potential

We investigate asymptotic safety of a toy model of a singlet-scalar extension of the Higgs sector including two real scalar fields under the impact of quantum-gravity fluctuations. Employing functional renormalization group techniques, we search for fixed points of the system which provide a tentative ultraviolet completion of the system. We find that in a particular regime of the gravitational parameter space the canonically marginal and relevant couplings in the scalar sector -- including the mass parameters -- become irrelevant at the ultraviolet fixed point. The infrared potential for the two scalars that can be reached from that fixed point is fully predicted and features no free parameters. In the remainder of the gravitational parameter space, the values of the quartic couplings in our model are predicted. In light of these results, we discuss whether the singlet-scalar could be a dark-matter candidate. Furthermore, we highlight how "classical scale invariance" in the sense of a flat potential of the scalar sector at the Planck scale could arise as a consequence of asymptotic safety.

hep-th↗

arXiv2018

Asymptotic safety in the dark

We explore the Renormalization Group flow of massive uncharged fermions -- a candidate for dark matter -- coupled to a scalar field through a Higgs portal. We find that fermionic fluctuations can lower the bound on the scalar mass that arises from vacuum stability. Further, we discuss that despite the perturbative nonrenormalizability of the model, it could be ultraviolet complete at an asymptotically safe fixed point. In our approximation, this simple model exhibits two mechanisms for asymptotic safety: a balance of fermionic and bosonic fluctuations generates a fixed point in the scalar self-interaction; asymptotic safety in the portal coupling is triggered through a balance of canonical scaling and quantum fluctuations. As a consequence of asymptotic safety in the dark sector, the low-energy value of the portal coupling could become a function of the dark fermion mass and the scalar mass, thereby reducing the viable parameter space of the model.

hep-ph↗

arXiv2017

Top mass from asymptotic safety

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 $M_\text{t,pole} \approx 171\, \rm GeV$.

hep-th↗

arXiv2017

Viability of quantum-gravity induced ultraviolet completions for matter

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 quantum-gravity 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.

gr-qc↗

arXiv2017

Quantum-gravity predictions for the fine-structure constant

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled.

hep-th↗

arXiv2017

Towards coarse graining of discrete Lorentzian quantum gravity

A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the number of discrete elements. To that end, the space of actions for causal set quantum gravity is written in a matrix-model-like language, and a flow equation for the effective action of the model is derived from the path integral.

gr-qc↗

arXiv2017

Upper bound on the Abelian gauge coupling from asymptotic safety

We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.

hep-th↗

arXiv2017

Status of the asymptotic safety paradigm for quantum gravity and matter

In the asymptotic safety paradigm, a quantum field theory reaches a regime with quantum scale invariance in the ultraviolet, which is described by an interacting fixed point of the Renormalization Group. Compelling hints for the viability of asymptotic safety in quantum gravity exist, mainly obtained from applications of the functional Renormalization Group. The impact of asymptotically safe quantum fluctuations of gravity at and beyond the Planck scale could at the same time induce an ultraviolet completion for the Standard Model of particle physics with high predictive power.

gr-qc↗

arXiv2017

An asymptotically safe solution to the U(1) triviality problem

We explore whether quantum gravity effects within the asymptotic safety paradigm can provide a predictive ultraviolet completion for Abelian gauge theories. We evaluate the effect of quantum gravity fluctuations on the running couplings in the gauge sector and discover an asymptotically safe fixed point of the Renormalization Group. In particular, if the strength of gravitational interactions remains below a critical strength, the minimal gauge coupling becomes asymptotically free. Further, we point out that a completely asymptotically free dynamics for the gauge field is impossible to achieve, as asymptotically safe quantum gravity necessarily induces nonvanishing higher-order interactions for the gauge field in the ultraviolet.

hep-th↗

arXiv2017

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

We explore whether perturbative interacting fixed points in matter systems can persist under the impact of quantum gravity. We first focus on semi-simple gauge theories and show that the leading order gravity contribution evaluated within the functional Renormalization Group framework preserves the perturbative fixed-point structure in these models discovered in [1]. We highlight that the quantum-gravity contribution alters the scaling dimension of the gauge coupling, such that the system exhibits an effective dimensional reduction. We secondly explore the effect of metric fluctuations on asymptotically safe gauge-Yukawa systems which feature an asymptotically safe fixed point [2]. The same effective dimensional reduction that takes effect in pure gauge theories also impacts gauge-Yukawa systems. There, it appears to lead to a split of the degenerate free fixed point into an interacting infrared attractive fixed point and a partially ultraviolet attractive free fixed point. The quantum-gravity induced infrared fixed point moves towards the asymptotically safe fixed point of the matter system, and annihilates it at a critical value of the gravity coupling. Even after that fixed-point annihilation, graviton effects leave behind new partially interacting fixed points for the matter sector.

hep-th↗

arXiv2017

Echoes of Asymptotic Silence in Causal Set Quantum Gravity

We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behaviour akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between causal set elements in the discrete analogue of a spatial hypersurface. Using numerical simulations for causal sets approximated by D=2,3 and 4 dimensional Minkowski spacetime, we show that while the discrete distance rapidly converges to the continuum distance at a scale roughly an order of magnitude larger than the discreteness scale, it is significantly larger on small scales. This allows us to define an effective dimension which exhibits dimensional reduction in the ultraviolet, while monotonically increasing to the continuum dimension with increasing continuum distance. We interpret these findings as manifestations of asymptotic silence in causal set theory.

gr-qc↗

arXiv2017

Flowing to the continuum in discrete tensor models for quantum gravity

Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size N serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for three-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.

gr-qc↗

arXiv2016

Quantum gravity and Standard-Model-like fermions

We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmetry.

gr-qc↗

arXiv2016

Quantum-gravity effects on a Higgs-Yukawa model

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.

hep-th↗

arXiv2016

Universal behavior of coupled order parameters below three dimensions

We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to bicritical or tetracritical behavior. Employing novel, pseudo-spectral techniques to solve functional Renormalization Group equations in a two-dimensional field space, we uncover a more intricate structure of fixed points in d<3, where two additional bicritical fixed points play a role. Towards d=2, we discover ranges of N=M with several simultaneously stable fixed points, indicating the coexistence of several universality classes.

cond-mat.stat-mech↗

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

Critical O(N) models above four dimensions: Small-N solutions and stability

We explore O(N) models in dimensions $4<d<6$. Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction. Recent results in $d=6-ε$ have uncovered an interacting ultraviolet fixed point of the renormalization group (RG) if the number N of components of the vector field is large enough, suggesting that these models are asymptotically safe. We set up a functional RG analysis of these systems to address three key issues: Firstly, we find that in $d=5$ the interacting fixed point exists all the way down to N=1. Secondly, we show that the standard O(N) universality classes are actually embedded in those of the cubic models, in that the latter exhibit the same values for (most of) the critical exponents, but feature an additional third RG relevant direction. Thirdly, we address the critical question of global stability of the fixed-point potential to test whether the fixed point can underly a viable quantum field theory.

hep-th↗

arXiv2016

Discovering and quantifying nontrivial fixed points in multi-field models

We use the functional renormalization group and the $ε$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed point solutions for the regime of small $N_i$. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points.

cond-mat.stat-mech↗