Off-shell divergences in perturbative quantum gravity

• Tim Morris

We investigate off-shell perturbative renormalisation of pure quantum gravity for both background metric and quantum fluctuations. We show that at each new loop order, the divergences that do not vanish on-shell are constructed from only the total metric, whilst those that vanish on-shell are renormalised by canonical transformations involving the quantum fields. Purely background metric divergences do not separately appear, and the background metric does not get renormalised. We highlight that renormalisation group identities play a crucial role ensuring consistency in the renormalisation of BRST transformations beyond one loop order. We verify these assertions by computing leading off-shell divergences to two loops, exploiting off-shell BRST invariance and the renormalisation group equations. Although some divergences can be absorbed by field redefinitions, we explain why this does not lead to finite beta-functions for the corresponding field.

The UV critical manifold of AS: news from the frontline

• Alfio Bonanno

RG and scattering in a shift-invariant scalar theory

• Roberto Percacci

Observables and Observers in Quantum Spacetime

• Renata Ferrero

Geometrical information of the quantum spacetime which we try to observe is crucially carried by physical fields. Geometrical observables cannot be properties of the “quantum spacetime” alone, but must also depend on the experimental setup that is used in order to observe or probe them. Every physics-based geometry will depend on the observer, and I will present two examples where this is manifest: I will employ the spectral flow method as a diagnostic tool to identify the scale-dependent field modes that participate in the geometric effective field theory; furthermore, I will present an approach to compute the RG flow of running relational observables in asymptotically safe quantum gravity.

From fluctuating gravitons to spectral functions

• Manuel Reichert

In this talk, I will review aspects of the fluctuation approach to metric quantum gravity. This approach disentangles dynamical metric fluctuations from the background metric, which allows to fulfil diffeomorphism symmetry constraints on the flow and to employ the systematic vertex expansion schemes. I will highlight important results such as momentum-dependent correlation functions at vanishing cutoff scale, the phase structure of the asymptotically safe Standard Model, and spectral properties of asymptotically safe gravity from direct computations in space-times with Lorentzian signatures such as the graviton spectral function.

Functional renormalisation for higher curvature quantum gravity

• Daniel Litim

TBA

Operator product expansion coefficient from the functional renormalization group

• Carlo Pagani

We present how to compute operator product expansion (OPE) coefficients within the functional renormalization group framework. After a brief introduction, we discuss how to extract the OPE coefficients from a three-point function by introducing sources conjugate to composite operators. Within this framework, we show how to recover the results known from the epsilon-expansion and how to obtain non-perturbative estimates.

Towards understanding the predictivety of asymptotically safe f(R)-gravity

• Maximilian Becker

In this talk, I compare two complementary ways of calculating critical exponents in the f(R)-truncation. The first of these is the standard way employed in FRG-based calculations, in which the couplings' anomalous dimensions are functions of the couplings themselves. The second way amounts to calculating critical exponents for a given fixed value of the couplings' anomalous dimensions. On a technical level, these can be obtained using a composite-operator FRG equation. The results for both calculation paths agree only for small order in the polynomial-R truncation and deviate from each other substantially for larger-order polynomial-R truncations. I will give an insight into why that is the case and will outline implications for the predictivety of the f(R)-truncation.

Some thoughts on gauge invariance and functional identities within functional renormalization

• Antonio Pereira (remote)

One of the most important structural aspects of functional renormalization techniques in the context of gauge theories is how to control gauge dependence along the flow. This is typically reduced to the discussion of gauge-parameter dependence. In some situations, with (quantum) gravity being a paradigmatic example, the use of a background-field gauge fixing is very convenient. Thus, background-field dependence is intimately related to gauge dependence. In this talk, I will present some thoughts on the use of dressed gauge fields in order to establish a connection between gauge-fixed flow equations with gauge-invariant proposals in the case of Yang-Mills theories and how to potentially generalize to quantum gravity. Moreover, I will introduce the concept of extended modified Slavnov-Taylor identity which controls gauge-parameter and background-field dependencies in a single functional identity instead of the usual separation between Slavnov-Taylor and Split Ward identities.

A lapse Wick rotation for the Functional Renormalization Group

• Max Niedermaier (remote)

A Wick rotation in the lapse (not in time) is introduced for all foliated metric geometries that leads to admissible complex metrics dampening the exponential of the action. Starting from a Euclidean signature scalar field FRG a well-defined Wick rotated version arises that covers the near Lorentzian regime. Augmenting the mathematical toolbox, a near Lorentzian counterpart of the heat kernel is rigorously constructed along these lines, whose asymptotic expansion allows one to control the ultraviolet aspects of the FRG solutions for strictly Lorentzian signature. The asymptotic expansion of the Wick rotated heat kernel induces the Hadamard parametrix for the Green's function associated with it via Laplace transform. However, not all physically relevant Green's functions arise in this way. A perspective on a stand-alone Green's function variant of the formalism is outlined for Bianchi I cosmological backgrounds.

Lorentzian asymptotic safety on curved backgrounds

• Kasia Rejzner (remote)

In this talk I will present recent results obtained with d'Angelo, Drago and Pinamonti. We have formulated flow equations on a very general class of Lorentzian manifolds and for a large class of physically interesting states. These equations resemble Wetterich equations and can be taken as a starting point for investigating asymptotic safety. The key ingredient is the use of the perturbative algebraic quantum field theory, which I will also review in my talk.

Asymptotically safe gravity-matter systems: functional and lattice perspectives

• Marc Schiffer

In this talk I will explore the interplay of quantum gravity with matter using functional and lattice methods. First, I will present recent FRG results on quantum gravity coupled to shift symmetric scalar fields. There, we find further indications that scalar self-interactions are induced by gravity, but that the previously explored weak-gravity bound might be spurious. Then, I will give a brief introduction to Euclidean dynamical triangulations and highlight how non-dynamical scalar fields can be used to investigate whether Euclidean dynamical triangulations, are a suitable tool to investigate asymptotic safety. Finally I will provide an outlook on using EDT and FRG in a concerted way to further explore the interplay of asymptotically safe quantum gravity with matter.

Exploring the asymptotically safe landscape

• Rafael Lino dos Santos (remote)

In this talk, I will explore the landscape of asymptotically safe quantum gravity. This landscape comprises theories that are made ultraviolet complete by asymptotic safety and are consistent with phenomenology at infrared scales. Despite many systematic uncertainties, I will discuss how this approach is helpful to connect physics at incredibly distant energy scales with a few new physics examples motivated by the dark universe and beyond Standard Model searches.

Asymptotic Safety in Gravity-Matter systems

• Jan Pawlowski (remote)

Massless and Partially Massless Limits in Quadratic Gravity

• Luca Buoninfante

In the context of perturbative quantum field theory, the addition of quadratic-curvature invariants to the Einstein-Hilbert action makes it possible to achieve strict renormalizability in four dimensions. The additional quadratic terms are multiplied by dimensionless coefficients that are related to the masses of the extra gravitational degrees of freedom and to the interaction couplings. The aim of this talk is to analyse the limit of the theory in which the Weyl-squared coefficient tends to infinity. Remarkably, the result of this limit turns out to be sensitive to the presence of a cosmological constant: when the latter is zero we have a massless limit for the spin-2 ghost, while when the cosmological constant is different from zero we obtain a partially massless limit. We show that the renormalizability property and the ghost-like nature of the massive spin-2 field ensure that the two limits do not hit strong couplings, unlike standard ghost-free theories of massive gravity. In particular, in the partially massless limit the interactions mediated by the spin-2 sector vanish. We argue that our results can be useful for understanding the high-energy limit of Quadratic Gravity. This talk is based on arXiv:2308.11324.

The non-perturbative S-matrix Bootstrap

• João Penedones (remote)

I will briefly review the recent revival of the non-perturbative S-matrix Bootstrap program. The current methods will be illustrated on two applications: (super)graviton scattering and a novel lower bound on the a-anomaly of 4D Conformal Field Theories.

Recent progress on the Cosmological Bootstrap

• Enrico Pajer (remote)

In this talk, I will review the cosmological bootstrap approach to the study of cosmological correlators from inflation, in which symmetries and general physical principles such as causality, unitarity and locality substitute the traditional model-building and lead to a variety of general results and new predictions for primordial signals. The object of study is the field theoretic wavefunction and its wavefunction coefficients, from which all correlators can be (perturbatively) derived. Wavefunction coefficients are the close analog of amplitudes in flat space and many results for amplitudes have avatars in the cosmological bootstrap. In the first part of the talk, I will review a few core results: (i) Causality implies that "off-shell" wavefunction coefficients (a.k.a. cosmological "in-out" Green's function) are analytic functions of off-shell energies (non-perturbatively) in the lower-half complex plane, whose singularity on the negative real axis are classified. (ii) Unitarity implies an infinite set of relations between higher and lower order contributions in perturbation theory known collectively as the cosmological optical theorem. (iii) Manifest locality constraints wavefunction coefficients in the form of analytically-continued soft limits. In the second part of the talk, I present a few poster children of this new approach: (1) The tree-level scalar bispectrum to all orders in derivatives; (2) The only three possible tree-level shapes of the parity-odd tensor bispectrum; (3) a no-go theorem for the parity-odd trispectrum and some yes-go examples and (4) the graviton trispectrum in general relativity.

Spacetime topology change and cobordism currents

• Ivano Basile

Examining spacetime topology change in quantum gravity leads to the triviality of cobordism classes: all transitions are allowed. This strong requirement entails the existence of extended objects, bundles of geometry carrying topological currents on their worldvolumes. Generally, the precise form of such currents is not very constrained. I will present a novel idea on how to fix their precise form when topological charges are encoded in more refined (co)homology theories. In the case of K-theory, topological currents characteristic of D-branes and O-planes arise from this bottom-up approach.

What are degrees of freedom in gravity?

• Masatoshi Yamada

In low energy, the gravitational force is well-described by the metric field (spin-2 symmetric tensor field). A question here is whether such a field is fundamental or not. In this talk, we discuss several possibilities that tensorial degrees of freedom emerge from matter. As examples, we are going to introduce the TTbar deformed scalar theory and fermion-induced gravity.

Essential Quantum Einstein Gravity

• Kevin Falls (remote)

In this talk I will discuss a simper picture of asymptotic safety based on an effective action that only contains the "essential" couplings that cannot be removed by a change of variables. This has technical advantages since the propagator can be ensured to take a more manageable form i.e. without developing additional poles. Using this approach the Reuter fixed point appears stable when extending the approximation. Furthermore, the results suggest that Newton's constant is the only relevant essential coupling in the absence of matter. On the conceptual side, this line of investigation hints that only the degrees of freedom of classical general relativity are necessary for its UV completion.

Towards a quantitative phenomenology of quantum gravity

• Aaron Held

I will discuss how the Renormalization Group (RG) flow of a surprisingly complete effective field theory (EFT) of nature opens up an opportunity for quantitative quantum-gravity phenomenology. With this goal in mind, my talk reviews phenomenological consistency constraints in (i) cosmology, (ii) particle physics, and (iii) black-hole astronomy. Taken together, these provide a highly nontrivial test for any predictive quantum-gravity scenario. Focusing on the asymptotic safety programme, I will highlight that the existence of an interacting fixed point of the RG flow places nontrivial bounds on the global RG flow in the EFT of nature. If asymptotic safety is regarded as fundamental, this implies enhanced predictive power. Even if asymptotic safety is regarded only as effective, boundary surfaces in the global RG flow impact phenomenological consistency.

Corrections to Schwarzschild geometry from the two-loop counterterm

• Cristobal Laporte

The quantization of general relativity predicts corrections to the gravitational dynamics. The most prominent local correction, which is non-vanishing in a vacuum, is the two-loop counterterm identified by Goroff and Sagnotti. In this talk, I will discuss how this correction term manifests itself in the Schwarzschild geometry, inducing wormholes and non-Schwarzschild black holes with cosmological horizons. Remarkably, its inclusion in the gravitational dynamics does not generate quantum hair – asymptotically flat, static, spherical solutions are still determined in terms of a single parameter, the asymptotic mass.

Functional renormalisation for cosmology

• Christof Wetterich

The evolution of our Universe in cosmic time is determined by a scaling solution of the functional renormalisation flow associated to a fixed point. Scaling solutions are highly predictive since they have to cover the whole field range for the effective scalar potential or the whole momentum range for the graviton propagator. For a given particle content quantum gravity fixes cosmology in terms of at most a few relevant parameters. We discuss the possibility that the dominant relevant mass scale for deviations from the scaling solution is substantially below the eV scale. In this case the Planck mass and particle masses arise from spontaneous breaking of quantum scale symmetry by the cosmological value of a scalar field. The scaling potential for this field predicts both inflation and dynamical dark energy. This setting solves the cosmological constant problem without any tuning of parameters.