Ivan Agullo

**Event horizons are tunable factories of quantum entanglement**

That event horizons generate quantum correlations via the Hawking effect is well known. In this talk, I will argue that the creation of entanglement can be modulated as desired, by appropriately illuminating the horizon. I will adapt techniques from quantum information theory to quantify the entanglement produced during the Hawking process and show that, while ambient thermal noise (e.g., CMB radiation) degrades it, the use of squeezed inputs can boost the non-separability genrated by the emiision of Hawking quanta in a controlled manner. I will further apply these ideas to analog event horizons concocted in the laboratory and insist that the ability to tune the generation of entanglement offers a promising route towards detecting quantum signatures of the elusive Hawking effect. More generally, the ideas presented here have direct application to the discussion of the information loss paradox. Partially based on Phys.Rev.Lett. 128 (2022) 9, 091301 2107.10217 [gr-qc].

Abhay Ashtekar

**Perspectives on Emergent Space-time**

Space-time metric and Einstein’s equations lie at the foundation of general relativity (GR). However, one can start with a a diff-invariant gauge theory that has never heard of a metric, write down the simplest equations one can, and show that Riemannian geometry and Einstein’s equations emerge by setting up an appropriate dictionary. While LQG was founded on this general idea, the force of its implications are not well appreciated because one generally begins with GR and reformulates it as connection-dynamics. Taking the gauge theory perspective as fundamental from the start provides new insights. In particular, time evolution of the gravitational field can be re-expressed as (a gauge covariant generalization of) the Lie derivative along a novel shift vector field in spatial directions. Thus, the canonical transformation generated by the Hamiltonian constraint acquires a geometrical interpretation on the gauge theory phase space, similar to that generated by the diffeomorphism constraint. The infinite dimensional Lie algebras that emerge may well have ramifications to some of the major thrusts of research such as the ‘double copy’ approach to scattering amplitudes, classification of 4-manifolds, and the role of volume preserving diffeomorphisms in gravity. As will be clear from Varadarajan’s talk, this viewpoint also opens a promising avenue to obtaining an anomaly-free algebra of quantum constraints in the canonical approach.

Eugenio Bianchi

**Typical entanglement in quantum gravity**

Miguel Campiglia

**Symmetries of asymptotically flat spacetimes**

I will review the link between symmetries of asymptotically flat spacetimes and the low frequency limit of gravitational radiation. Building on well-established results, I will present several open problems and current efforts towards their resolution.

Sylvain Carrozza

**Group Field Theory renormalization: A brief overview**

The idea of the renormalization group has proven essential to the establishment of quantum field theory as a viable framework for high energy physics, and is by now a pillar of modern physics. We may therefore expect it to survive, in some form or another, in any satisfactory theory of quantum gravity. It is nonetheless clear that, by relying on a background notion of space-time scale, the hierarchical description of phenomena on which renormalization is usually based needs some rethinking in this regime. In this talk, I will provide an overview of renormalization group methods tailored to Group Field Theories (GFTs). Just as with ordinary quantum field theories, perturbative renormalization is essential to establish the internal consistency and predictive power of a GFT, and can be proven rigorously (at least in simple toy-models). Understanding non-perturbative properties of a GFT is much more challenging, but aspects of this question have been approached by means of truncated functional renormalization group flows. In the long run, it is hoped that renormalization methods will help unravel the phase structure of GFTs, and in particular, allow to prove that general relativity can be recovered in a suitable limit.

Bianca Dittrich

**Modified general relativity from the continuum limit of effective spin foams**

Effective spin foams have been introduced to facilitate the extraction of dynamical information from the spin foam path integral. In this talk I will illustrate that effective spin foams have delivered on this promise: I will review how effective spin foams provided a transparent explanation of how the flatness problem of spin foams is avoided in the discrete. With some assumptions on the spin foam path integral, the effective spin foam approach can be also used to determine the continuum limit of spin foam dynamics. To leading order the dynamics is given by a massless graviton, but includes corrections arising from the emergence of an effective area metric. I will then derive the same dynamics directly from a modified Plebanski action. This does provide strong evidence that spin foams reproduce general relativity in the continuum limit and opens new avenues to study the phenomenological implications of spin foams.

Pietro Dona

**Numerical evaluation of spin foam transition amplitudes**

In recent years numerics proved to be a fantastic tool for studying spin foam theories. This talk will review the state-of-the-art technology to evaluate spin foam amplitudes numerically. We will overview its main applications and possible improvements.

Jonathan Engle

**The flatness (non-)problem in spin-foams and its significance**

In this talk, I give an overview of work that has been done on the so-called flatness problem in spin-foam models. There are various versions of the flatness problem that have been derived in the literature, with various levels of rigor. There are also multiple works explaining why this is not a problem with the spin-foam model per se, but rather with the limit being taken - specifically, the taking of the semiclassical limit prior to taking the refinement limit. I will summarize all of this, as well as giving my own viewpoint on the significance of these works for future research in spin-foams.

Laurent Freidel

**A new paradigm for quantum gravity based on symmetry**

In this introductory talk, I will mention the past successes but also review what are the shortcomings of loop gravity and spin foam models that needs to be addressed in order to be able to claim the models we have provide a theory of quantum gravity. I will present a new perspective about quantum gravity which aims to address these shortcomings. This new approach is deeply rooted in a renewed understanding of local symmetries in Gravity. It focuses first on the understanding of how gravitational systems decompose into subsystems. It also provides a detailed description of the nature of entanglement of gravitational subsystems. I will emphasize the central role of the corner symmetry group in capturing all the necessary data needed to glue back seamlessly quantum spacetime regions. I will explain how this picture extends the classical loop gravity framework and provide radical new insight into the nature of quantum geometry and the role of the Immirzi parameter. I will show how this approach allows us to have a quantum representation of infinitesimal diffeomorphism and associated new quantum numbers. I will also show how these ideas provide a new non-perturbative definition of quantum radiation. If time permits, I will show how these ideas naturally allow to connect semi-classical gravitational physics, S-matrix theory, and non-perturbative quantum gravity results.

Kristina Giesel

**Reduced phase space quantisation in loop quantum gravity**

In this talk an overview over existing results that apply a reduced phase space quantisation to formulate the dynamics of loop quantum gravity will be presented. It will be briefly reviewed how a reduced phase space for GR can be derived by coupling additional reference matter. In the framework of the relational formalism this corresponds to choosing classical matter clocks and solving the corresponding constraints at the classical level. The reduced phase space for GR is taking as a starting point for a loop quantisation either in full LQG or in symmetry reduced models as for instance in LQC where in both cases the quantum theory is formulated at the level of the physical Hilbert space and the dynamics is generated by a physical Hamiltonian. Different choices of reference matter yield in general different quantum models and some of the existing models will be compared. Finally, it will be briefly discussed how this quantisation procedure can be also applied in the context of open quantum systems involving gravity using geometrical clocks.

Muxin Han

**Covariant Loop Quantum Gravity**

This talk discusses the recent advances in the covariant formulation of Loop Quantum Gravity (LQG), and in particular, the spinfoam theory. The discussions include the analytic and numerical studies of the spinfoam amplitudes, the large-j semiclassical analysis, and the spinfoam model with cosmological constant. If time permits, this talk will also discuss the recent path integral formulation of LQG relating to the reduced phase quantization.

Philipp Hoehn

**Dynamical frame covariance**

Employing dynamical reference frames for providing gauge-invariant internal descriptions of the physics has become a standard in gravity. However, dynamical frames are also crucial in gauge theories (e.g. as edge modes) and in quantum foundations in the absence of external relata. A central question is how the descriptions relative to different frame choices are related, especially in the quantum theory where such frames can be in relative superposition. In this talk, I will describe a dynamical version of frame covariance that answers this question in a unifying manner. Importantly, this leads to a gauge-invariant, but frame-dependent notion of subsystems, which in the quantum theory implies frame-dependent correlations and thermal properties. I will then sketch a completely general framework for constructing relational observables in generally covariant theories that unifies previous approaches and naturally comes with the notion of relational atlases and dynamical frame transformations. This can be viewed as establishing a genuinely relational -- and thus arguably more physical -- update of the usual notion of general covariance. Time permitting, I will also comment on a relational form of microcausality.

Mercedes Martin-Benito

**Cosmological Perturbations in Loop Quantum Cosmology**

The introduction of cosmological perturbations in cosmological models within Loop Quantum Cosmology (LQC) is a natural and necessary step when working towards a falsifiable picture of the theory. This talk is a review of the physical predictions obtained when considering primordial cosmological perturbations in the context of LQC. One important question that we will analyze is the choice of initial conditions (or vacuum state) for the perturbations, reviewing how the different choices proposed within the LQC framework get along with observations.

Daniele Oriti

**Cosmology from full quantum gravity, in the group field theory formalism**

We survey recent progress concerning the extraction of cosmological dynamics from full quantum gravity. Cosmology is described in terms of relational observables, in an hydrodynamics approximation to the fundamental quantum gravity dynamics, taking the form of a non-linear extension of quantum cosmology. This progress mostly took place within the group field theory formalism, thus with immediate implications for loop quantum gravity and spin foam models, but most of the insights so obtained have more general validity for quantum gravity. We review both key results of direct cosmological interest (on singularity resolution and semi-classical limit, dark energy and cosmological perturbations, relational dynamics, effective methods), as well as those supporting them indirectly and concerning the quantum gravity formalism itself. We also clarify the broader perspective motivating this research direction and the tools used, as well as possible future developments.

Javier Olmedo

**Kruskal Black Holes in Loop Quantum Gravity: Recent advances**

In this talk we will review several properties of some recent effective geometries for macroscopic Kruskal spacetimes within an improved dynamics scheme similar to the one of loop quantum cosmology. In particular, they share several features: (a) the classical singularity `inside' the horizon is naturally resolved; (b) high curvature regions are regular and connect trapped and anti-trapped regions; (c) at low curvatures, quantum effects are negligible for macroscopic black holes. We discuss the advantages and limitations of these proposals. Finally, we show that quasinormal modes of these geometries show deviations with respect to the classical theory, for instance, breaking the isospectralty between axial and polar modes. However, these deviations are negligibly small for macroscopic black holes.

Daniele Pranzetti

**Higher spin symmetry in gravity from asymptotic Einstein's equations**

I will first show how the leading Einstein equations in a large-r expansion around null infinity can be derived and recast in a compact form by relying uniquely on the transformation properties under the corner symmetry group at scri, the so-called Weyl BMS group. In addition to the to spin-0 and spin-1 gravitational charges related to the Bondi mass and angular momentum, this analysis reveals the existence of a spin-2 charge. I will review how these charge Ward identities are equivalent to the soft graviton theorems. Motivated by the infinite towers of soft symmetries recently uncovered in celestial holography, I will extend the recursion relation defining the gravitational charge dynamics to higher spins. I will provide evidence that this recursion relation for higher spin charges corresponds to a truncation of the evolution equations for all subleading terms in the Weyl scalar encoding incoming radiation. Moreover, I will show that these asymptotic charges form a representation of a w_{1+\infty} algebra on the gravitational phase space.

Carlo Rovelli

**Loop quantum Gravity: present and future**

I review main ideas, achievements, and open challenges, for the best tentative theory we have today for describing the quantum behaviour of spacetime.

Neil Turok

**Gravitational Entropy and the Large Scale Geometry of Spacetime**

I’ll review a new, simpler explanation for the large scale geometry of spacetime, presented recently by Latham Boyle and me in arXiv:2201.07279. The basic ingredients are elementary and well-known, namely Einstein’s theory of gravity and Hawking’s method of computing gravitational entropy. The new twist is provided by the boundary conditions we proposed for big bang-type singularities, respecting CPT and conformal symmetry (traceless matter stress energy) as well as analyticity at the bang. These boundary conditions allow gravitational instantons for universes with positive Lambda, massless (exactly conformal) radiation and positive or negative space curvature. Using these new instantons, we are able to infer the gravitational entropy for a complete set of quasi-realistic, four-dimensional cosmologies. If the total entropy in radiation exceeds that of Einstein’s static universe, the gravitational entropy exceeds the famous de Sitter entropy. As it increases further, the most probable large-scale geometry becomes increasingly flat, homogeneous and isotropic. I’ll summarize recent progress towards elaborating this picture into a fully predictive cosmological theory.

Madhavan Varadarajan

**LQG Dynamics: An Electric Shift in Perspective**

Classical time evolution of the Ashtekar variables admits an elegant re-expression in terms of their generalized Lie derivatives with respect to a spatial vector field triple called the Electric Shift. In Euclidean gravity this property of classical evolution naturally dovetails into a construction of quantum dynamics which reveals itself to be devoid of Perez's spin $j$ ambiguity. Strong evidence exists for the spacetime covariant nature of the quantum dynamics so constructed as well as for its ability to propagate quantum gravitational perturbations. Arguably, we are now tantalizingly close to a construction of physical states of Lorentzian quantum gravity via Thiemann's `Wick' rotation of their Euclidean counterparts. In this talk I will discuss work done over the last decade which is supportive of this picture of LQG dynamics.

Cong Zhang

**Fermions coupling in Loop Quantum Gravity and Resolution of Doubling Problem**

The canonical formulation of fermion coupled to loop quantum gravity is investigated and applied to reconstruct the quantum fermion field theory in Minkowski spacetime. In our model, the complexifier coherent states averaged over various graphs are employed to resemble the classical background. Then, taking advantage of our formulation, we compute the two-point correlation function explicitly. The resulting two-point correlation function turns out to carry a correct semiclassical limit. In other works, the doubling problem appearing in lattice QFT is resolved by our model.