Asymptotic Safety Research Articles

Harvesting physical predictions from asymptotically safe quantum field theories

Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges on an interacting fixed point of the Wilsonian renormalization group flow which controls the microscopic dynamics. Connecting the fixed point to observations requires constructing the set of effective actions compatible with this microscopic dynamics. Technically, this information is stored in the UV-critical surface of the fixed point. In this work, we describe a novel approach for extracting this information based on analytical and pseudospectral methods. Our construction is illustrated at the level of the three-dimensional Ising model and easily generalizes to any asymptotically safe quantum field theory. It also constitutes an important step toward setting up a well-founded swampland program within the gravitational asymptotic safety program. Published by the American Physical Society 2024

The shadow and gamma-ray bursts of a Schwarzschild black hole in asymptotic safety

Abstract The effects and rules of the dimensionless parameter $\xi$ on neutrino annihilation $\nu+\bar{\nu}\to e^{-}+e^{+}$ dominated gamma-ray bursts are analysed and investigated within the context of black holes in asymptotic safety. We also computationally model photon orbits around black holes, as photons and neutrinos have the same geodesic equations near black holes. We show that the black hole shadow radius decreases with increasing $\xi$. Calculations are made to determine the temperature of the accretion disk surrounding the black hole and the ratio $\dot{Q}/\dot{Q}_{Newt}$ of energy deposition per unit time to that of the Newtonian scenario. The accretion disk temperature peaks at a higher temperature due to quantum gravity corrections, which increases the probability of neutrino emission from the black hole. It is interesting to note that larger quantum gravity effects cause the ratio value to significantly decline. In the neutrino-antineutrino annihilation process, the energy deposition rate is sufficient even while the energy conversion is inhibited because of quantum corrections. Gamma-ray bursts might originate from the corrected annihilation process. Additionally, we examine the derivative $\mathrm{d}\dot{Q}/\mathrm{d}r$ about the star radius $r$. The findings demonstrate that the ratio is lowered by the black hole's quantum influence. The neutrino pair annihilation grows weaker the more prominent the influence of quantum gravity is.

Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.

Non-Hermitian lattice fermions in the 2D Gross-Neveu-Yukawa model

We work the lattice fermions and non-Hermitian formulation in the 2D Gross-Neveu-Yukawa (GNY) model and demonstrate the numerical implementation for two flavors by the hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the nonsymmetrized finite-difference operator. We restore the hypercubic symmetry by averaging over all possible orientations with the proper continuum limit. Our study is the first simulation for the interacting fermion formulated in a non-Hermitian way. We compare the numerical solution with the one-loop resummation. The resummation results matches with the numerical solution in ⟨ϕ⟩, ⟨ϕ2⟩, ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)/2⟩, and ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)ϕ/2⟩. We also used the one-loop resummation to provide the renormalization group flow and asymptotic safety in the 2D GNY model. Published by the American Physical Society 2024

Momentum-dependent field redefinitions in asymptotic safety

We discuss general momentum-dependent field redefinitions in the context of quantum-gravitational scattering amplitudes in general, and asymptotic safety in particular. Implementing such redefinitions at the lowest curvature order, we can bring the graviton propagator into tree-level form, avoiding issues of fiducial ghost poles and their associated violations of unitarity. We compute the beta function for Newton’s constant, and find an asymptotically safe fixed point whose critical exponent changes by 0.4% compared to not resolving the momentum-dependent field redefinition. This provides a strong indication that this fixed point does not feature extra degrees of freedom related to ghostly modes, and has a good chance of being related to a unitary theory. Published by the American Physical Society 2024

Quantum gravity modifications to the accretion onto a Kerr black hole

In the framework of the Asymptotic Safety scenario for quantum gravity, we analyze quantum gravity modifications to the thermal characteristics of a thin accretion disk spiraling around a renormalization group improved (RGI-) Kerr black hole in the low energy regime. We focused on the quantum effects on the location of the innermost stable circular orbit (ISCO), the energy flux from the disk, the disk temperature, the observed redshifted luminosity, and the accretion efficiency. The deviations from the classical general relativity due to quantum effects are described for a free parameter that arises in the improved Kerr metric as a consequence of the fact that the Newton constant turns into a running coupling G(r) depending on the energy scale. We find that, both for rapid and slow rotating black holes with accretion disks in prograde and retrograde circulation, increases in the value of this parameter are accompanied by a decreasing of the ISCO, by a lifting of the peaks of the radiation properties of the disk and by an increase of the accretion mass efficiency, as compared with the predictions of general relativity. Our results confirm previously established findings in Zuluaga and Sánchez (Eur Phys J C 81:840, 2021) where we showed that these quantum gravity effects also occur for an accretion disk around a RGI-Schwarzschild black hole.

Global flows of foliated gravity-matter systems

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation structure by encoding the gravitational degrees of freedom in a lapse function, shift vector, and a metric measuring distances on the spatial slices. We use the Wetterich equation to study the renormalization group flow of the graviton 2-point function extracted from the spatial metric. The flow is driven by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert action supplemented by minimally coupled scalar and vector fields. We derive bounds on the number of matter fields cast by asymptotic safety. Moreover, we show that the phase diagram obtained in the pure gravity case is qualitatively stable within these bounds. An intriguing feature is the presence of an IR-fixed point for the graviton mass which prevents the squared mass taking negative values. This feature persists for any number of matter fields and, in particular, also in situations where there is no suitable interacting fixed point rendering the theory asymptotically safe. Our work complements earlier studies of the subject by taking contributions from the matter fields into account.

Asymptotic safety in the Litim-Sannino model at four loops

Asymptotic safety in the Litim-Sannino model at four loops

Asymptotic safety in Lorentzian quantum gravity

A recently introduced functional renormalization group (RG) provides a new tool to explore nonperturbative and covariant RG flows in Lorentzian spacetimes. We apply it for the first time to investigate the ultraviolet limit of quantum gravity. While the RG flow is state dependent, it is possible to evaluate state- and background-independent contributions to the flow. Taking into account only these universal terms, the RG flow exhibits a nontrivial fixed point in the Einstein-Hilbert truncation, providing a mechanism for asymptotic safety in Lorentzian quantum gravity. Published by the American Physical Society 2024

Searching for singlet vector-like leptons via pair production at ILC

Vector-like leptons (VLLs) as one kind of the most intriguing particles, have been widely concerned in several extensions of the Standard Model (SM). In this work, we explore the discovery potential of VLLs via pair production in the context of models that satisfy asymptotic safety at the International Linear Collider (ILC). The expected sensitivities of the ILC with the center of mass energy s=1 TeV and the integrated luminosity L=1 ab−1 to the parameter space of this kind of VLL models are derived. The results we obtained show that, for the VLL with mass MF in the region of MF∈[101 GeV,463 GeV], the Yukawa coupling κ can be as low as κ∈[0.032,0.098].

Black strings in asymptotically safe gravity

In this paper, we study black strings in asymptotic safety gravity (ASG) scenario. The ASG approach is introduced by implementing gravitational and cosmological running coupling constants directly in the black string metric. We calculate the Hawking temperature, entropy, and heat capacity of the improved black string metric in two cases: considering the cosmological constant fixed in some fixed point and the general case where both Newton’s constant and cosmological constant are improved. For the identification of the scale moment we used an general inverse law setting k(r) ∼ 1/r n . We show that improving only the Newton’s constant the problem of singularity is solved for the identifications with n > 1. However, if the cosmological constant is also running the singularity persists in the solution. Also, we show that the ASG effects predicts the presence of a remnant mass in the final evaporation process. Besides that, a logarithmic correction is observed in the entropy. However, a running cosmological constant introduces new correction terms to the entropy beyond that. We show that the improved black string solution remains stable, as in the usual case. Phase transitions are not observed in both cases studied here.

Dust Collapse in Asymptotic Safety: A Path to Regular Black Holes.

Regular black hole spacetimes are obtained from an effective Lagrangian for quantum Einstein gravity. The interior matter is modeled as a dust fluid, which interacts with the geometry through a multiplicative coupling function denoted as χ. The specific functional form of χ is deduced from asymptotically safe gravity, under the key assumption that the Reuter fixed point remains minimally affected by the presence of matter. As a consequence the gravitational coupling vanishes at high energies. The static exterior geometry of the black hole is entirely determined by the junction conditions at the boundary surface. Consequently, the resulting global spacetime geometry remains devoid of singularities at all times. This outcome offers a new perspective on how regular black holes are formed through gravitational collapse.

Shadow and photon ring of black hole in asymptotically safe gravity

In this paper, we discuss the influence of thin disk accretion and asymptotically safe (AS) gravity correction parameters on the shadow and photon ring of black hole. For the thin disk accretion, the dark region is the shadow of the black hole, and the bright photon ring is composed of direct image, lensing ring, and photon ring. For the specific intensity of the radiation source of the accretion disk, we consider three different emission profile models. For the second-order attenuation function model in which the emission starts from the innermost circular orbit, direct image, lensing ring, and photon ring can be clearly distinguished. The direct image contributes most of the brightness, and the lensing ring contributes a small portion, while the contribution of the photon ring can almost be ignored. And the observed corresponding intensity peak decreases with the increase of the AS gravity parameter, that is, the corresponding brightness of the photon ring darkens as correction parameter increases. For the third-order attenuation function model in which the emission begins at the radius of the photon sphere, lensing ring and photon ring are superimposed on the direct radiation. Thus a new extreme value of the observed intensity emerges, and the extreme value increases with the increase of the AS gravity parameter, which leads to a brighter observed photon ring. For the anti-trigonometric attenuation function model in which the radiation starts from the event horizon, the superposition range of lensing ring and photon ring on the direct radiation becomes larger, which makes photon ring wider. The smaller the AS gravity parameter, the more difficult it is to distinguish between the lensing ring and photon ring, and the brighter the photon ring turns. In short, the results show that the shadow radius decreases with the increase of the AS correction parameter. For different AS gravity correction parameters, the light intensities of emission source, especially emission profiles of the observed intensity are significantly different, resulting in obvious differences in observed emission intensity between the shadow of the black hole and the bright photon ring of the black hole.

Regular black hole from a confined spin connection in Poincaré gauge gravity

Within the asymptotic safety program, it is possible to construct renormalization group (RG) improved spacetimes by replacing the gravitational coupling G by its running counterpart G(k), and subsequently identifying the RG scale k with a physical distance scale. This procedure has been used to construct a regular Schwarzschild geometry, but it fails in the presence of a cosmological constant. This can only be avoided if the dimensionless cosmological constant has a trivial ultraviolet fixed point, but so far no such scenario has been encountered in quantum general relativity (with or without matter). In this Letter we provide a possible solution to this problem. In Poincaré gauge gravity an effective cosmological constant arises naturally, and if the non-Abelian Lorentz spin connection is asymptotically free, it generates a trivial ultraviolet fixed point for this cosmological constant. We thereby tentatively propose a nonsingular black hole consistent with the principles of asymptotic safety, embedded in Poincaré gauge gravity.

One-loop beta-functions of quartic enhanced tensor field theories

Enhanced tensor field theories (eTFTs) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the universal geometry found for tensor models. For generic order d of the tensor field, we compute the perturbative β-functions at one-loop of two just-renormalizable quartic eTFT coined by + or ×, depending on their vertex weights. The models + has two quartic coupling constants , and two 2-point couplings (mass, Za ). Meanwhile, the model × has two quartic coupling constants and three 2-point couplings (mass, Za , ). At all orders, both models have a constant wave function renormalization: Z = 1 and therefore no anomalous dimension. Despite such peculiar behavior, both models acquire nontrivial radiative corrections for the coupling constants. The RG flow of the model + exhibits a particular asymptotic safety: is marginal without corrections thus is a fixed point of arbitrary constant value. All remaining couplings determine relevant directions and get suppressed in the UV. Concerning the model ×, is marginal and again a fixed point (arbitrary constant value), λ, µ and Za are all relevant couplings and flow to 0. Meanwhile is a marginal coupling and becomes a linear function of the time scale. This model can neither be called asymptotically safe or free.

Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures

We revisit the dynamical generation of an arbitrarily small neutrino Yukawa coupling in the Standard Model with trans-Planckian asymptotic safety and apply the same mechanism to the gauged B − L model. We show that thanks to the presence of additional irrelevant couplings, the described neutrino-mass generation in the B − L model is potentially more in line with existing theoretical calculations in quantum gravity. Interestingly, the model can accommodate, in full naturalness and without extensions, the possibility of purely Dirac, pseudo-Dirac, and Majorana neutrinos with any see-saw scale. We investigate eventual distinctive signatures of these cases in the detection of gravitational waves from first-order phase transitions. We find that, while it is easy to produce a signal observable in new-generation space interferometers, its discriminating features are washed out by the strong dependence of the gravitational-wave spectrum on the relevant parameters of the scalar potential.

Asymptotic safety guaranteed at four-loop order

Asymptotic safety guaranteed at four-loop order

Foliated asymptotically safe gravity in the fluctuation approach

The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key step in this program is the transition from Euclidean to Lorentzian signature spacetimes. One way to address this challenge is to formulate the quantum theory based on the Arnowitt-Deser-Misner decomposition of the metric field. This equips the Euclidean spacetime with a preferred direction which may serve as the time-direction in the Lorentzian setting. In this work we use the Wetterich equation in order to compute the renormalization group flow of the graviton two-point function. The resulting beta functions possess a non-Gaussian renormalization group fixed point suitable for rendering the theory asymptotically safe. The phase diagram underlying the flow of the two-point function is governed by the interplay between this non-Gaussian fixed point, the Gaussian fixed point, and an infrared fixed point. The latter ensures that the renormalized squared graviton mass cannot take negative values. These results are in qualitative agreement with fluctuation computations carried out in the covariant setting. We take this as non-trivial evidence that the asymptotic safety mechanism remains intact when considering quantum gravity on spacetimes carrying a foliation structure. Technically, our work constitutes the first fluctuation computation carried out within the ADM-framework. Therefore, we also provide a detailed discussion of the conceptual framework, highlighting the elements which differ from fluctuation computations in the covariant setting.

Investigating the connection between generalized uncertainty principle and asymptotically safe gravity in black hole signatures through shadow and quasinormal modes

The links between the deformation parameter beta of the generalized uncertainty principle (GUP) to the two free parameters hat{omega } and gamma of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program, has been conducted recently in [Phys. Rev. D 105 (2022) 12, 124054. https://doi.org/10.1103/PhysRevD.105.124054] In this paper, we test these findings by calculating and examining the shadow and quasinormal modes of black holes, and demonstrate that the approach provides a theoretical framework for exploring the interplay between quantum gravity and GUP. Our results confirm the consistency of ASG and GUP, and offer new insights into the nature of black holes and their signatures. The implications of these findings for future studies in quantum gravity are also discussed.

Perturbative Asymptotic Safety and Its Phenomenological Applications

Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group (RG) flow, and generalize well-known asymptotic freedom to a scale-invariant ultraviolet completion with non-vanishing interactions. In this review, we discuss the key ideas behind asymptotic safety, a mechanism for achieving it, and the conditions it imposes on general gauge–Yukawa field theories. We also pay special attention to possible phenomenological applications and provide an overview of standard model (SM) extensions potentially exhibiting asymptotic safety.