**Abstract:**

We investigate signal propagation in a quantum field simulator of the Klein–Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system’s boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of nonequilibrium field dynamics in general space–time metrics.

**M. Tajik, M. Gluza, N. Sebe, P. Schüttelkopf, F. Cataldini, J. Sabino, F. Møller, S.-C. Ji,
S. Erne, G. Guarnieri, S. Sotiriadis, J. Eisert, J. Schmiedmayer, “Experimental observation of curved light-cones in a quantum field simulator”, PNAS 120, (2023).**

https://www.pnas.org/doi/10.1073/pnas.2301287120

Related to Project A03

**Abstract:**

Quantum entanglement has been identified as a crucial concept underlying many intriguing phenomena in condensed matter systems such as topological phases or many-body localization. Recently, instead of considering mere quantifiers of entanglement like entanglement entropy, the study of entanglement structure in terms of the entanglement spectrum has shifted into the focus leading to new insights into fractional quantum Hall states and topological insulators, among others. What remains a challenge is the experimental detection of such fine-grained properties of quantum systems. The development of protocols for detecting features of the entanglement spectrum in cold atom systems, which are one of the leading platforms for quantum simulation, is thus highly desirable and will open up new avenues for experimentally exploring quantum many-body physics. Here we present a method to bound the width of the entanglement spectrum, or entanglement dimension, of cold atoms in lattice geometries, requiring only measurements in two experimentally accessible bases and utilizing ballistic time-of-flight (ToF) expansion. Building on previous proposals for entanglement certification for photon pairs, we first consider entanglement between two atoms of different atomic species and later generalize to higher numbers of atoms per species and multispecies configurations showing multipartite high-dimensional entanglement. Through numerical simulations we show that our method is robust against typical experimental noise effects and thus will enable high-dimensional entanglement certification in systems of up to 8 atoms using currently available experimental techniques.

**N. Euler, M. Gärttner, “Detecting high-dimensional entanglement in cold-atom quantum simulators”, arXiv:2305.07413 (2023).**

https://arxiv.org/abs/2305.07413

Related to Project A06

**Abstract:**

We present our experimental and theoretical framework, which combines a broadband superluminescent diode with fast learning algorithms to provide speed and accuracy improvements for the optimization of on-dimensional optical dipole potentials, here generated with a digital micromirror device. To characterize the setup and potential speckle patterns arising from coherence, we compare the superluminescent diode to a single-mode laser by investigating interference properties. We employ machine-learning tools to train a physics-inspired model acting as a digital twin of the optical system predicting the behavior of the optical apparatus including all its imperfections. Implementing an iterative algorithm based on iterative learning control we optimize optical potentials an order of magnitude faster than heuristic optimization methods. We compare iterative model-based “offline” optimization and experimental feedback-based “online” optimization. Our methods provide a route to fast optimization of optical potentials, which is relevant for the dynamical manipulation of ultracold gases.

**M. Calzavara, Y. Kuriatnikov, A. Deutschmann-Olek, F. Motzoi, S. Erne, A. Kugi, T. Calarco, J. Schmiedmayer, M. Prüfer, “Optimizing Optical Potentials With Physics-Inspired Learning Algorithms”, Phys. Rev. Appl. 19 (2023).**

https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.044090

Related to Project A03

**Abstract:**

The theoretical understanding of scaling laws of entropies and mutual information has led to substantial advances in the study of correlated states of matter, quantum field theory and gravity. Experimentally measuring von Neumann entropy in quantum many-body systems is challenging, as it requires complete knowledge of the density matrix, which normally requires the implementation of full state reconstruction techniques. Here we measure the von Neumann entropy of spatially extended subsystems in an ultracold atom simulator of one-dimensional quantum field theories. We experimentally verify one of the fundamental properties of equilibrium states of gapped quantum many-body systems—the area law of quantum mutual information. We also study the dependence of mutual information on temperature and on the separation between the subsystems. Our work represents a step towards employing ultracold atom simulators to probe entanglement in quantum field theories.

**M. Tajik, I. Kukuljan, S. Sotiriadis, B. Rauer, T. Schweigler, F. Cataldini, J. Sabino, F. Møller, P. Schüttelkopf, Si-Cong Ji, D. Sels, E. Demler, J. Schmiedmayer, “Experimental verification of the area law of mutual information in a quantum field simulator”, Nature Phys., (2023).
**

https://www.nature.com/articles/s41567-023-02027-1

Related to Project A03

**Abstract:**

Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behavior in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarize corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective-action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarize the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.

**A. N. Mikheev, I. Siovitz, T. Gasenzer, “Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium”, arXiv:2304.12464 (2023).**

https://arxiv.org/abs/2304.12464

Related to Project A04

**Abstract:**

Universal scaling dynamics of a many-body system far from equilibrium signals the proximity of the time-evolution to a non-thermal fixed point. We find universal dynamics connected with rogue-wave like events in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these caustics is affected by the time varying spatial correlation length of the potential, giving rise to an additional exponent $δ_{c}≃1/3$ for temporal scaling, which is different by a factor $∼4/3$ from the exponent $β_{V}≃1/4$ characterizing the scaling of the correlation length $_{V}∼t_{βV}$ with time. As a result of the caustics, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations determining the frequency of instanton events to occur scale in time as $t_{δI}$. This suggests that the universality class of a non-thermal fixed point could be characterized by different, mutually related exponents defining the coarsening evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early universe to geophysical dynamics and micro physics.

**I. Siovitz, S. Lannig, Y. Deller, H. Strobel, M.K. Oberthaler, T. Gasenzer, “Universal dynamics of rogue waves in a quenched spinor Bose condensate”, arXiv:2304.09293 (2023).**

https://arxiv.org/abs/2304.09293

Related to Project A04

**Abstract:**

Numerical simulations of the full quantum properties of interacting many-body systems by means of field-theoretic Monte-Carlo techniques are often limited due to a sign problem. Here we simulate properties of a dilute two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) transition by means of the Complex Langevin (CL) algorithm, thereby extending our previous CL study of the three-dimensional Bose gas to the lower-dimensional case. The purpose of the paper is twofold. On the one hand, it adds to benchmarking of the CL method and thus contributes to further exploring the range of applicability of the method. With the respective results, the universality of the equation of state is recovered, as well as the long-wave-length power-law dependence of the single-particle momentum spectrum below the BKT transition. Analysis of the rotational part of the current density corroborates vortex unbinding in crossing the transition. Beyond these measures of consistency we compute quantum corrections to the critical density and chemical potential in the weakly coupled regime. Our results show a shift of these quantities to lower values as compared to those obtained from classical field theory. It points in the opposite direction as compared to the shift of the critical density found by means of the path-integral Monte-Carlo method at larger values of the coupling. Our simulations widen the perspective for precision comparisons with experiment.

**P. Heinen, T. Gasenzer, “Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin”, arXiv:2304.05699 (2023).**

https://arxiv.org/abs/2304.05699

Related to Project A04

**Abstract:**

We present the first direct and nonperturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel Lorentzian renormalization group approach, combined with a spectral representation of correlation functions. We find a positive graviton spectral function, showing a massless one-graviton peak and a multigraviton continuum with an asymptotically safe scaling for large spectral values. We also study the impact of a cosmological constant. Further steps to investigate scattering processes and unitarity in asymptotically safe quantum gravity are indicated.

**J. Fehre, D. F. Litim, J. M. Pawlowski, M. Reichert, “Lorentzian Quantum Gravity and the Graviton Spectral Function”, Phys.Rev.Lett. 130 (2023).**

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.081501

Related to Project A02

**Abstract:**

The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena. A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics. In our experiment, we demonstrate that such a 1D behavior can extend much further into the dimensional crossover toward 3D than expected. Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate the dynamics of a single density mode. Employing the theory of generalized hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities. Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one dimensionality where thermalization should occur. We attribute our observations to an emergent Pauli blocking of transverse excitations caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic. Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations. More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions.

**F. Cataldini, F. Møller, M. Tajik, J. Sabino, S.-C. Ji, I. Mazets, T. Schweigler, B. Rauer, J.
Schmiedmayer, “Emergent Pauli Blocking in a Weakly Interacting Bose Gas”, Phys. Rev. X 12 (2022).**

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041032

Related to Project A03

**Abstract:**

We discuss the emergence of a low-energy effective theory with quarks, mesons, diquarks and baryons at vanishing and finite baryon density from first principle QCD. The present work also includes an overview on diquarks at vanishing and finite density, and elucidates the physics of transitional changes from baryonic matter to quark matter including diquarks. This set-up is discussed within the functional renormalisation group approach with dynamical hadronisation. In this framework it is detailed how mesons, diquarks, and baryons emerge dynamically from the renormalisation flow of the QCD effective action. Moreover, the fundamental degrees of freedom of QCD, quarks and gluons, decouple from the dynamics of QCD below the respective mass gaps. The resulting global picture unifies the different low energy effective theories used for low and high densities within QCD, and allows for a determination of the respective low energy constants directly from QCD.

**K. Fukushima, J. M. Pawlowski, N. Strodthoff, “Emergent Hadrons and Diquarks”, Annals Phys. 446, 169106 (2022).**

https://www.sciencedirect.com/science/article/pii/S0003491622002093?via%3Dihub

Related to Project A02

**Abstract:**

We compute high-order baryon number fluctuations at finite temperature and density within a QCD-assisted low energy effective field theory. Quantum, thermal and density fluctuations are incorporated with the functional renormalization group approach. Quantum and in-medium fluctuations are encoded via the evolution of renormalization group flow equations. The resulting fourth- and sixth-order baryon number fluctuations meet the lattice benchmark results at vanishing density. They are consistent with experimental measurements, and in particular, the non-monotonic dependence of the kurtosis of net-baryon number distributions on the collision energy is observed in our calculations. This non-monotonicity arises from the increasingly sharpened chiral crossover with the decrease of collision energy.

**W. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, R. Wen, S. Yin, “High-order baryon number
fluctuations within the fRG approach”, PoS CPOD2021, 009 (2022).**

Related to Project A02

**Abstract:**

Near the second order phase transition point, QCD with two flavours of massless quarks can be approximated by an O(4) model, where a symmetry breaking external field H can be added to play the role of quark mass.

The Lee-Yang theorem states that the equation of state in this model has a branch cut along the imaginary H axis for |Im[H]|>Hc, where Hc indicates a second order critical point.

This point, known as Lee-Yang edge singularity, is of importance to the thermodynamics of the system.

We report here on ongoing work to determine the location of Hc via complex Langevin simulations.

**F. Attanasio, M. Bauer, L. Kades, J. M. Pawlowski, “Searching for Yang-Lee zeros in O(N)
models”, PoS LATTICE2021, 223 (2022).**

Related to Project A02

**Abstract:**

We determine the chiral phase structure of (2+1)-flavor QCD in dependence of temperature and the light flavor quark mass with Dyson-Schwinger equations. Specifically, we compute the renormalized chiral condensate and its susceptibility. The latter is used to determine the (pseudo)critical temperature for general light current quark masses. In the chiral limit we obtain a critical temperature of about 141 MeV. This result is in quantitative agreement with recent functional renormalization group results in QCD and is compatible with the respective lattice results. We also compute the order parameter potential of the light chiral condensate, map out the regime in the phase diagram which exhibits quasi-massless modes, and discuss the respective chiral dynamics.

**F. Gao, J. M. Pawlowski, “Phase structure of (2+1)-flavor QCD and the magnetic equation of state”, ****Physical Review D** **105****, (2022).**

https://onlinelibrary.wiley.com/doi/full/10.1002/piuz.202370204

Related to Project A02

**Abstract:**

Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromodynamics at finite density to the nonequilibrium evolution of quantum systems. Many computational approaches have been developed for tackling the sign problem emerging for complex actions. Among these, complex Langevin dynamics has the appeal of general applicability. One of its key challenges is the potential convergence of the dynamics to unphysical fixed points. The statistical sampling process at such a fixed point is not based on the physical action and hence leads to wrong predictions. Moreover, its unphysical nature is hard to detect due to the implicit nature of the process. In the present work we set up a general approach based on a Markov chain Monte Carlo scheme in an extended state space. In this approach we derive an explicit real sampling process for generalized complex Langevin dynamics. Subject to a set of constraints, this sampling process is the physical one. These constraints originate from the detailed-balance equations satisfied by the Monte Carlo scheme. This allows us to rederive complex Langevin dynamics from a new perspective and establishes a framework for the explicit construction of new sampling schemes for complex actions.

**L. Kades, M. Gärttner, T. Gasenzer, J. M. Pawlowski, “Monte Carlo sampling of complex
actions in extended state spaces”, Phys. Rev. E 105, 045315 (2022).**

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.045315

Related to Project A02

**Abstract:**

We reconstruct ghost and gluon spectral functions in 2+1 flavor QCD with Gaussian process regression. This framework allows us to largely suppress spurious oscillations and other common reconstruction artifacts by specifying generic magnitude and length scale parameters in the kernel function. The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point. For the infrared and ultraviolet extensions of the lattice propagators as well as the low-frequency asymptotics of the ghost spectral function, we utilize results from functional computations in Yang-Mills theory and QCD. This further reduces the systematic error significantly. Our numerical results are compared against a direct real-time functional computation of the ghost and an earlier reconstruction of the gluon in Yang-Mills theory. The systematic approach presented in this work offers a promising route toward unveiling real-time properties of QCD.

**J. Horak, J. M. Pawlowski, J. Rodríguez-Quintero, J. Turnwald, J. M. Urban, N. Wink, S.
Zafeiropoulos, “Reconstructing QCD spectral functions with Gaussian processes”, Phys. Rev. D 105, (2022).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.036014

Related to Project A02

**Abstract:**

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

**A. Bonanno, T. Denz, J. M. Pawlowski, M. Reichert, “Reconstructing the graviton”, SciPost Phys. 12, 1 (2022).**

https://scipost.org/10.21468/SciPostPhys.12.1.001

Related to Project A02, B03, C01

**Abstract:**

A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborate the findings of earlier works, namely that the mass gap generation is tied to the longitudinal projection of the gluon self-energy, which acts as an effective mass term in the equations. Because an explicit mass term is in conflict with gauge invariance, this leaves two possible scenarios: If it is viewed as an artifact, only the scaling solution survives; if it is dynamical, gauge invariance can only be preserved if there are longitudinal massless poles in either of the vertices. We find that there is indeed a massless pole in the ghost-gluon vertex, however in our approximation with the assumption of complete infrared dominance of the ghost this pole is only present for the scaling solution. We also put forward a possible mechanism that may reconcile the scaling solution, with an infrared dominance of the ghost, with the decoupling solutions based on longitudinal poles in the three-gluon vertex as seen in the PT-BFM scheme.

**G. Eichmann, J. M. Pawlowski, J. M. Silva, “Mass generation in Landau-gauge Yang-Mills
theory”, Phys. Rev. D 104, 114016 (2021).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.114016

Related to Project A02

**Abstract:**

In local scalar quantum field theories at finite temperature correlation functions are known to satisfy certain nonperturbative constraints, which for two-point functions in particular implies the existence of a generalization of the standard Källén-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, η0. As an example, we calculate η0 in ϕ4 theory, establishing its leading behavior in the small and large coupling regimes.

**P. Lowdon, R.-A. Tripolt, J. M. Pawlowski, D. H. Rischke, “Spectral representation of the shear viscosity for local scalar QFTs at finite temperature”, Phys. Rev. D 104, 065010 (2021).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.065010

Related to Project A02

**Abstract:**

We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter 0<ξ≤5. Extrapolating the propagators to ξ→∞, we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values ξ≲1/2 of the gauge-fixing parameter. It is shown that the correlation functions, and, in particular, the ghost propagator, change significantly with increasing gauge parameter. In turn, the ghost-gluon running coupling as well as the position of the zero crossing of the Schwinger function of the gluon propagator remain within the uncertainties of our calculation unchanged.

**M. Napetschnig, R. Alkofer, M. Q. Huber, J. M. Pawlowski, “Yang-mills propagators in linear covariant gauges from nielsen identities”, Phys. Rev. D 104, 054003 (2021).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.054003

Related to Project A02

**Abstract:**

We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field theoretical description of strongly coupled systems. In particular, we exploit the exact 2PI relations between the two-point and four-point functions in order to truncate the infinite hierarchy of equations of the functional renormalization group. The truncation is ”exact” in two ways. First, the solution of the resulting flow equation is independent of the choice of the regulator. Second, this solution coincides with that of the 2PI equations for the two-point and the four-point functions, for any selection of two-skeleton diagrams characterizing a so-called Ф-derivable approximation. The transformation of the equations of the 2PI formalism into flow equations offers new ways to solve these equations in practice, and provides new insight on certain aspects of their renormalization. It also opens the possibility to develop approximation schemes going beyond the strict Ф-derivable ones, as well as new truncation schemes for the fRG hierarchy.

**U. Reinosa, J.-P. Blaizot, J. M. Pawlowski, “Functional renormalization group and 2PI effective action formalism”, Annals Phys. 431, 168549 (2021).**

https://www.sciencedirect.com/science/article/pii/S000349162100155X?via%3Dihub

Related to Project A02

**Abstract:**

We present a comprehensive study of the quark sector of 2+1 flavor QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex in the one-loop dressed approximation. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with 2+1 dynamical quark flavors, obtained from studies with Schwinger-Dyson equations, the functional renormalization group approach, and large volume lattice simulations. The appropriate renormalization procedure required in order to self-consistently accommodate external inputs stemming from other functional approaches or the lattice is discussed in detail, and the value of the gauge coupling is accurately determined at two vastly separated renormalization group scales. Our analysis establishes a clear hierarchy among the vertex form factors. We identify only three dominant ones, in agreement with previous results. The components of the quark propagator obtained from our approach are in excellent agreement with the results from Schwinger-Dyson equations, the functional renormalization group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as (245 MeV)3. The present approach has a wide range of applications, including the self-consistent computation of bound-state properties and finite temperature and density physics, which are briefly discussed.

**F. Gao, J. Papavassiliou, J. M. Pawlowski, “Fully coupled functional equations for the quark sector of QCD”, Phys. Rev. D 103, 094013 (2021).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.094013

Related to Project A02

**Abstract:**

We propose a novel simulation strategy for Yang-Mills theories with a complex coupling, based on the Lefschetz thimble decomposition. We envisage that the approach developed in the present work can also be adapted to QCD at finite density and real-time simulations. Simulations with Lefschetz thimbles offer a potential solution to sign problems in Monte Carlo calculations within many different models with complex actions. We discuss the structure of generalized Lefschetz thimbles for pure Yang-Mills theories with a complex gauge coupling β and show how to incorporate the gauge orbits. We propose to simulate such theories on the union of the tangential manifolds to the relevant Lefschetz thimbles attached to the critical manifolds of the Yang-Mills action. We demonstrate our algorithm on a (1+1)-dimensional U(1) model and discuss how, starting from the main thimble result, successive subleading thimbles can be taken into account via a reweighting approach. While we face a residual sign problem, our novel approach performs exponentially better than the standard reweighting approach.

**J. M. Pawlowski, M. Scherzer, C. Schmidt, F. P. G. Ziegler, F. Ziesché, “Simulating Yang-Mills theories with a complex coupling”, Phys. Rev. D 103, 094505 (2021).**

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.094505

Related to Project A02

**Abstract:**

In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalization group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art in pure gravity and general gravity–matter systems. This includes the discussion of results on the existence and properties of the asymptotically safe ultraviolet fixed point, full ultraviolet-infrared trajectories with classical gravity in the infrared, and the curvature dependence of couplings also in gravity–matter systems. The results in gravity–matter systems concern the ultraviolet stability of the fixed point and the dominance of gravity fluctuations in minimally coupled gravity–matter systems. Furthermore, we discuss important physics properties such as locality of the theory, diffeomorphism invariance, background independence, unitarity, and access to observables, as well as open challenges.

**J. M. Pawlowski, M. Reichert, “Quantum Gravity: A Fluctuating Point of View”, Front. in
Phys. 8, 551848 (2021).**

https://www.frontiersin.org/articles/10.3389/fphy.2020.551848/full

Related to Project A02