

Plenary talks:
THOMAS THIEMANN (FriedrichAlexander University ErlangenNürnberg), Review Talk on Canonical Loop Quantum Gravity
The purpose of this talk is to summarise the status of the canonical formulation of Loop Quantum Gravity.
YONGGE MA (Beijing Normal University), Recent advances on the Hamiltonian constraint operator in LQG (Slides)
We will review the recent progress on the Hamiltonian constraint operator in loop quantum gravity, including the regularization method with less ambiguity and Hilbert spaces where symmetric Hamiltonian constraint operators can be well defined. Some proposals on how to solve the Hamiltonian constraint and how to investigate its semiclassical limit will also be addressed.
CARLO ROVELLI (CPT Marseille), How to compute a realistically observable quantity in LQG: the black hole lifetime
Ultimately, we must learn how to use a quantum gravity theory for computing realistic observables and compare them with actual observations. This is a task infamously plagued by difficulties that are not just technical but also conceptual. Here I show a concrete example where these difficulties can be concretely addressed in LQG: the computation of the lifetime of a black hole. This is a quantity that is observable in principle, and that might even be measurable in practice.
DANIELE ORITI (AEI Potsdam), Group field theory: where from and where to (Slides)
We outline the basic ingredients of the group field theory (GFT) formalism for quantum gravity as a fieldtheoretic description of fundamentally discrete constituents of spacetime (spin networks or elementary simplices), clarifying its relation with loop quantum gravity, spin foam models, and random tensor models. We emphasise the role that this formalism plays in tackling some key open issues in the field, in particular concerning the regime of the theory involving many fundamental constituents of spacetime. Finally, we survey a number of recent research directions based on the GFT formalism, aimed at addressing these key open issues: GFT symmetries and inequivalent representations, GFT renormalization, GFT condensate cosmology, entanglement and holography in GFT states.
EDWARD WILSON EWING (University of New Brunswick), Testing loop quantum cosmology (Slides)
I will review the predictions of loop quantum cosmology for the cosmic microwave background in inflationary, matter bounce and ekpyrotic scenarios. In some cases loop quantum cosmology can modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensortoscalar ratio in the matter bounce scenario. Effects such as these are potential observational tests for loop quantum cosmology.
DANIELE PRANZETTI (SISSA), New boundary degrees of freedom (Slides)
I will present a purely algebraic derivation of new boundary degrees of freedom from the symplectic structure of first order gravity in presence of a generalization of the GibbonsHawkingYork boundary term including the Immirzi parameter. In the presence of a loop quantum gravity state encoding a locally flat (quantum) geometry, these boundary degrees of freedom localize along a set of punctures on the boundary sphere and their origin is due to the second class nature of the residual tangent diffeomorphisms. These degrees of freedom carry a representation of a twisted U(1)^3 KacMoody symmetry, encoding a Virasoro algebra and an SU(2) symmetry. These symmetries, attached at each puncture, generalize the SU(2) algebra associated to each link in loop gravity into an infinite dimensional algebra with central charge. Application to black hole entropy counting and implications for holographic entanglement ideas will also be discussed.
WILLIAM DONNELLY (University of California), Diffeomorphism invariance and the flat space limit (Slides)
Any quantum theory of gravity should reduce to local quantum field theory in a suitable limit. Yet quantum field theory is formulated in terms of algebras of local observables, while in quantum gravity diffeomorphism invariance forbids the existence of such local observables. I will show how to resolve this tension by constructing 'gravitationally dressed' diffeomorphisminvariant observables in perturbative gravity. These dressed observables reduce to the familiar local operators of quantum field theory in the weak gravity limit, but exhibit corrections to microcausality at leading order in Newton's constant. I will show that this degree of nonlocality is a necessary feature of all diffeomorphisminvariant observables, and argue that this has drastic consequences for the formulation of local subsystems.
Based on 1507.07921, 1607.01025 and 1706.03104 with Steve Giddings.
LAURENT FREIDEL (Perimeter Institute), Edge modes, symmetry and subsystems in Gauge theories (Slides)
In this talk I will present new understanding on old questions. How can we decompose a gauge theory in subsystems? what is the relationship between gauge and symmetries? How do we discretize gauge invariant systems? Is the Newtonian potential quantum or classical? and is the vacuum sector of relativistic massless theories unique?
We show that all these questions are intimately related to the presence of new degrees of freedom associated with the presence of boundaries regardless of whether they are finite or infinite. These edge modes, that appears in massless theories, are necessary in order to restore the gauge invariance of the theory and remarkably they reveal a new type of symmetry associated with an infinite number of conserved charge classically. We will exemplify these in the context of QED gravity and string theory where they lead to different physical effects. We will show how these can be used to create a fusion product that generalizes the tensor product.
BIANCA DITTRICH (Perimeter Institute), Bootstrapping quantum gravity (Slides)
Quantum gravity amplitudes, as e.g. formulated in the loop quantum gravity approach, have to satisfy certain consistency conditions in order to lead to a viable theory. I will present the consistent boundary framework in which these consistency conditions are central. I show how these conditions can be used in a bootstrap approach, which leads to the construction of consistent quantum gravity amplitudes in a truncation scheme. Here the truncation is informed by the dynamics of the system. This feature also ensures that the scheme corresponds to an expansion around a physically interesting state that can be identified with the physical vacuum state.
I will explain how this addresses the problem of the “continuum limit” for loop quantum gravity and why this represents a scheme in which the dynamics of quantum gravity can be addressed in a meaningful truncation.
SYLVAIN CARROZZA (Perimeter Institute), Spin foam renormalization à la GFT: status and prospects (Slides)
I will review the status of the Group Field Theory (GFT) renormalization programme, and its implications for spin foam models. Thanks to powerful techniques developed in the context of tensor models, it is now possible to construct explicit examples of wellbehaved GFTs on SU(2). These are genuine renormalizable quantum field theories (albeit nonlocal ones), which allow to rigorously organize the spin foam amplitudes into a perturbative sum. This is a crucial step which, in a more complete quantum gravity setting, would result in a consistent prescription for the sum over quantum spacetime histories. More recently, nonperturbative renormalization methods such as the Wetterich equation have been adapted to GFTs, thus opening the way to a systematic exploration of the phase diagram of these models. This approach should be especially relevant to recent cosmological applications of GFT condensate states, and more generally to the identification of physically interesting GFT phases. I will conclude with a list of open questions which need to be addressed in order to bridge the gap between the current technology and 4d quantum gravity proposals.
EMANUELE ALESCI (SISSA), QRLG, Statistical Regularization and the Bounce (Slides)
In this talk I will present the state of art of Quantum Reduced Loop Gravity, a gauge fixed version of LQG. The theory allow to construct kinematical states for gauge fixed metrics and to study the modified dynamics preserving the gauge fixing.
It has been applied to cosmology where the gauge fixed kinematical Hilbert space contains all the elements of the full theory in a simplified context: Diff invariant spinnetworks are replaced by reduced spinnetworks with matrix elements of geometrical and constraints operators analytically manageable. The study of its semiclassical limit using coherent states allows to reproduce Loop Quantum Cosmology results in the mu_0 a mubar scheme for Friedmann and Bianchi I models. In particular the graph structure allows to identify the two schemes as particular choices of density matrices controlling the quantum superposition over the graphs that identify homogeneous Universes. A general density matrix motivated by statistical arguments leads to what we call Statistical Regularization scheme. The study of the Statistical scheme shows new striking features for Friedmann: the Big Bounce scenario of LQC is replaced by the Emergent Bouncing Universe. Our classical Universe emerges with consecutive bounces followed by a last Big Bounce from a metastable quantum phase in which the Universe is confined in a scale of order 100 Planck volumes and gravitational attractive forces are dynamically competing with pure quantum gravity repulsive forces.
MAXIMILLIAN HANUSCH (University of Würzburg), Relating LQC with LQG: Algebraic Aspects (Slides)
We present recent developments in the understanding of symmetry reduction at the foundation of LQC with special focus on the results obtained in jointwork with Jonathan Engle and Thomas Thiemann. We introduce a new approach that makes the action of dilations well defined on the reduced quantum holonomy flux *algebra. We discuss uniqueness of the diffeomorphism invariant state on this algebra in the framework of homogeneous isotropic LQC; a result formerly obtained in the LOST paper for the quantum holonomy flux *algebra of full LQG; as well as in a paper by Ashtekar and Campiglia for Homogeneous LQC. In analogy to the results obtained there, we find that the GNSrepresentation that corresponds to the unique invariant state equals the standard representation used in homogeneous isotropic LQC so so far. Remarkably, this holds in both the standard case where holonomies only along straight curves are considered as well as in the Fleischhack case where all analytic curves are taken into account.
HERMAN VERLINDE (Princeton University), Strings and Loops: What can they learn from each other? (Slides)
In this talk I will describe how string theory and loop quantum gravity are two complementary approaches to the same problem. I will illustrate the two perspectives with the help of a toy example: the recently discovered microscopic realization of AdS2 holography via the SYKmodel. The relationship between gravity, black holes and quantum chaos plays a central role in the story.
MARC GEILLER (Perimeter Institute), New representations for quantum gravity (Slides)
It has been realized in recent years that, already at the kinematical level, the holonomyflux variables of LQG can describe different geometrical phases, which in turn give rise to inequivalent realizations of quantum geometry. This is rooted in the fact that LQG can be thought of as a topological quantum field theory with defects. In this talk, I will review the various technical and conceptual developments which have happened in this direction. This will cover in particular the socalled BF vacuum and representation, its extension to a nonvanishing cosmological constant via quantum groups, the definition of a new basis adapted to coarsegraining, and the construction of new 3+1 topological quantum field theories.
ETERA LIVINE (ENS Lyon), Dressed Spin Networks: from CoarseGraining to Holography in Loop Quantum Gravity (Slides)
I will discuss the coarsegraining of the algebraic and combinatorial data carried by spin network states and of the corresponding discrete geometry. I will review the recent proposals for dressed spin networks, enhanced with extra algebraic structure, and stress the notions of boundary states that they induce. This will underline the deep relation between coarsegraining and the implementation of the diffeomorphism constraints in the context of holography in loop quantum gravity.
MEHDI ASSANIOUSSI (University of Warsaw), On the dynamics of LQG deparametrized models: a perturbative approach (Slides)
An important aspect in understanding the dynamics in the context of deparametrized models of LQG is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. In this talk, I will briefly review the concept of deparametrization, some examples of LQG deparametrized models and the quantization of the physical Hamiltonians. Then I will focus on presenting a perturbative method to approximate the dynamics generated by a given physical Hamiltonian operator. This new method allows us to define an approximate spectral decomposition of the Hamiltonian operators, overcoming several technical obstacles in the explicit calculations within LQG deparametrized models. I will illustrate the utility of this approach in some explicit calculations of the evolution of some geometric observables in certain quantum models.
SIMONE SPEZIALE (CPT Marseille), LQG: A twistorial perspective
We review the status of the relation between loop quantum gravity and twistors, and discuss recent results and future directions for research.
WOLFGANG WIELAND (Perimeter Institute), New boundary variables for classical and quantum gravity (Slides)
In loop quantum gravity, we have a pretty good understanding of the quantum geometry in the bulk. What is missing is a clear picture of what is going on at boundaries, in particular boundaries that are null, which seems to be the most relevant case physically. In my talk, I present a series of results on this frontier: At the classical level, I consider general relativity in terms of selfdual variables in domains with inner null boundaries. At these null boundaries, a new pair of canonical variables appears, which consists of a spinor and a conjugate spinorvalued twoform. Using these boundary spinors, I discuss some aspects of the quantum theory, in particular the quantisation of area. In fact, the area of a twodimensional cross section has a discrete spectrum, and no spinnetworks or SU(2) variables are ever required for deriving this result. Finally, I present a proposal for how to formulate the dynamics for discretised gravity in terms of a topological field theory on a system of internal null boundaries.
JAMES SULLY (McGill University), Loop Equations for Gauge/Gravity Duality (Slides)
Gauge/gravity duality is a powerful, nonperturbative tool for studying quantum gravity. It gives a UV complete, backgroundindependent reformulation of gravitational observables in terms of an equivalent, dual conformal field theory (CFT). However, the dictionary between these equivalent theories is usually written in terms of perturbative, local operatorsand local operators are not good gravitational observables nor do they allow easy comparison with CFT calculations. I will outline an improved dictionary that matches simple backgroundindependent operators in the gravitational theory to natural building blocks of the CFT. In doing so, I will formulate novel 'loop equations' for the dynamics of gravitational and conformal field theories.
NELSON YOKOMIZO (Universidade Federal de Minas Gerais), Squeezed spin networks and entanglement (Slides)
We introduce squeezed spin network states as a new family of semiclassical states in loop quantum gravity. We review the construction and main properties of squeezed spin networks and discuss their application to the reconstruction of semiclassical geometries. A characteristic feature of macroscopic geometries is the area law for the entanglement entropy. We show that squeezed states can encode long range correlations in the fluctuations of the geometry that are associated with the emergence of an area law for the entropy.
FRANCESCA VIDOTTO (Radboud University Nijmegen), How to measure a realistically observable quantity in LQG: primordial black holes (Slides)
Quantumgravity are expected to resolve the singularity at the center of a black hole, but also to have dramatic effects on the dynamical horizon, eventually removing it in an explosive event. The timescale of such process is shorter than the evaporation time and is potentially at reach of observation: if black holes formed in the early universe, some would be exploding today. The associated electromagnetic emission could have different components, presenting theirselves as radio and TeV cosmic rays, with a distinctive energyredshift relation. As primordial black holes are considered as a possible constituent of dark matter, their quantumgravitational explosion would have consequences for the cosmological observation of the early universe, and for those of the late universe as well. This open the possibility to study quantumgravity effects on new observational windows.
PARAMPREET SINGH (Louisiana State University), Black hole bounce (Slides)
We will review some recent developments on the quantization of the Schwarzschild interior using techniques of loop quantum gravity. The underlying quantum geometric effects result in a singularity resolution and unlike previous attempts to quantize black hole interior a consistent quantization free of fiducial structure and yielding correct infrared limit can be obtained. Though as in the isotropic cosmological models one obtains a bounce, the bounce is not in general symmetric. Rather like anisotropic models, the bounce is asymmetric resulting in a difference between the mother black hole and the child white hole. We will discuss some phenomenological aspects of this quantization, numerical results on stability and some potential generalizations of the quantization.
DANIEL MARTÍN DE BLAS (Pontificia Universidad Católica de Chile), Hybrid LQC: choice of vacuum state for cosmological perturbations in LQC (Slides)
We discuss the important role played by the choice of a vacuum state for the cosmological perturbations in the predictions derived for the primordial power spectra, not only in LQC, but also in more standard treatments of the quantum perturbations. We focus our analysis on results obtained within the emph{hybrid quantization} approach, although most of our conclusions, if not all, can be extended to other approaches in LQC. We consider first several constructions of emph{adiabatic states}, and then we turn our attention to the study of the socalled emph{nonoscillatory} vacuum, recently proposed as a physically appealing alternative. Finally, we comment on other vacuum and quantization prescriptions that have been employed in the LQC literature, comparing the predictions that arise from these different proposals.
ANDREA DAPOR (FriedrichAlexander University ErlangenNürnberg), Rainbow metrics and effective cosmological models (Slides)
One of the main open problems of Quantum Gravity is how to recover a classical geometry in the macroscopic limit. A solution proposed in recent years relies on the concept of 'dressed metric', an effective classical spacetime emerging from the interaction between the quantum state of matter and the quantum state of gravity. We review these ideas with the use of an analogy, and discuss recent developments in the context of cosmology and rainbow metrics.
GIOVANNI AMELINOCAMELIA (Università di Roma “La Sapienza”), Probing quantumspacetime structure with GRB photons and neutrinos
For nearly two decades the possibility of probing shortdistance spacetime structure using photons and neutrinos from gammaray bursters has been intensely studied. Recently the quantity and quality of available data has improved significantly, allowing the relevant phenomenology to move forward from a previous phase based on noteworthy single events to a new phase based on statistical analyses over all observed GRBs. I give an overview of these recent developments. Intriguingly, the present data situation, while inconclusive, lends itself to interpretation in terms of dispersive propagation in a quantum spacetime.
MARCIN KISIELOWSKI (University of Warsaw), Asymptotic analysis of the EPRL vertex amplitude with timelike tetrahedra (Slides)
In the covariant Loop Quantum Gravity the dynamics of the spinnetwork states is given by a sum over quantum geometries of spacetime described by spin foams. A basic building block of a spinfoam transition amplitude is the socalled vertex amplitude. For example in PonzanoRegge spinfoam model a vertex amplitude is equal to a 6jsymbol, which is asymptotic in the large spin limit to a cosine of a discrete (Regge) action for 3D Euclidean Gravity. Generalizations of this symbol to the physical 4D Lorentzian theory have been proposed, the most promising being the EnglePereiraRovelliLivine vertex amplitude. In its original formulation it applies to geometries with spacelike tetrahedra only but it has been generalized by Conrady and Hnybida to include timelike tetrahedra as well. We will discuss the asymptotics of this extended vertex amplitude for large representation parameters.
SEBASTIAN STEINHAUS (University of Hamburg), Renormalizing spin foam models: quantum cuboids and beyond (Slides)
The refinement approach to renormalizing spin foam models has made significant progress in recent years. Its fundamental idea is to compare the same physical transition across discretisations of varying ‘fineness’ by identifying states in different (boundary) Hilbert spaces, similar to the AshtekarLewandowski construction in LQG. I will explain how this allows us to efficiently extract results and check their consistency. To reach these goals numerical techniques are indispensable. I will support this by presenting recent results, in particular the calculation of the first renormalization group flow of the (restricted) 4D Euclidean EPRL model, in which we found indications for an UVattractive fixed point. I will close with a brief outlook on future developments.
TATJANA VUKASINAC (Universidad Michoacana de San Nicolás de Hidalgo), 2D dilaton gravity theories in polartype variables: A review of some classical and quantum results (Slides)
I will consider a class of two dimensional dilaton gravity models, and revisit them from the perspective of a new set of polartype variables. These variables are a generalization of variables introduced within the spherically symmetric sector of 4D general relativity, adapted for a loop quantization. I will show that for a large class of models one can perform a series of canonical transformations in such a way that the Poisson algebra of the constraints becomes a Lie algebra. Loop quantization of these models has been performed for two particular cases: CGHS model and spherically symmetric 4D gravity and leads to a singularity resolution in the corresponding quantum theories. I will briefly review those developments.
STEPHEN GIELEN (Imperial College London), Cosmology from group field theory condensates (Slides)
I will review the idea that a macroscopic Universe like our own can be described as a condensate of LQG spin network vertices in group field theory (GFT). The kinematics and dynamics of the Universe then emerges from the hydrodynamic continuum approximation to the fundamental quantum GFT: cosmology is the "hydrodynamics of quantum gravity". I will motivate the idea from various considerations in classical and quantum gravity, and show its realisation in GFT: the hydrodynamic approximation connects the abstract grouptheoretic and combinatorial language of GFT (and LQG) to the spacetime physics of cosmology. More specifically, I will show that GFT condensates can give an understanding of various features of LQC effective dynamics, while also suggesting possible phenomenology beyond LQC. I will attempt to discuss most of the results of the last years in this field.
ALDO RIELLO (Perimeter Institute), Entanglement entropies in 3d gauge theories and quantum gravity
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, I introduce a new definition of entanglement entropy for both Abelian and non–Abelian gauge theories. I will then relate this construction to earlier proposals and argue that it brings these closer to each other. I will also point out that different definitions of entanglement entropies can be related to different choices of vacua (AL or BF) and excitations (electric or electromagnetic).Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, I introduce a new definition of entanglement entropy for both Abelian and non–Abelian gauge theories. I will then relate this construction to earlier proposals and argue that it brings these closer to each other. I will also point out that different definitions of entanglement entropies can be related to different choices of vacua (AL or BF) and excitations (electric or electromagnetic).
GOFFREDO CHIRCO (AEI Potsdam), Group field theory and tensor networks: holographic entanglement entropy in full quantum gravity (Slides)
We investigate the use of tensor networks techniques and quantum information theory for the study of the entanglement properties of quantum gravity states. In the language of the group field theory, we describe spin network states as quantum manybody systems. The very connectivity of such states, encoded in the links of the underlying graphs, is associated with the entanglement between the fundamental quanta constituting them. We establish a dictionary between group field theory states and (generalised) random tensor networks. With such a dictionary at hand, we target the calculation of the RyuTakayanagi formula for the entanglement entropy in the full quantum gravity formalism of group field theory.

