Welcome words

• Sijbrand deJong (Radboud University)

Room: Valkhofzaal

From the birth of CDT to a modified Friedmann equation that resolves the Hubble constant tension.

• Yoshiyuki Watabiki
• Jan Ambjorn (Niels Bohr Institute & Radboud University)

Room: Valkhofzaal We describe how the original 2d CDT model has been generalized in various ways: to a multicomponent W3 algebra model based on the exceptional Jordan algebra and to a four-dimensional CDT model. Remarkably, under certain assumptions, both these generalisations lead to the same modified Friedmann equation where the present expansion of our universe is driven not by the cosmological constant, but by the creation of baby universes. We will discuss how the model seems to resolve the tension between the Hubble constant determined from early time observations (the CMB data) and from present days local direct measurements.

Matter-driven change of spacetime topology in 4D CDT

• Andrzej Görlich (Jagiellonian University, Krakow)

Room: Valkhofzaal The model of Causal Dynamical Triangulations (CDT) is a background-independent and diffeomorphism-invariant approach to quantum gravity, which provides a lattice regularization of the formal gravitational path integral. The framework does not involve any coordinate system and employs only geometric invariants. For a Universe with toroidal spatial topology, we can introduce coordinates using classical scalar fields with periodic boundary conditions with a jump. The field configurations reveal pictures of cosmic voids and filaments surprisingly similar to the ones observed in the present-day Universe. I will discuss the impact of dynamical matter fields on the geometry of a typical quantum universe in the four-dimensional CDT model. I will also explain several observed phenomena, in particular, a phase transition triggered by the change of the scalar field jump amplitude. This discovery may have important consequences for quantum universes with non-trivial topology since the phase transition can change the topology to a simply connected one.

Q&A for both talks Room: Valkhofzaal

Causal Sets and the Continuum

• Steve Carlip (UC Davis)

Room: Valkhofzaal We understand reasonably well how to construct a discrete causal set that approximates a given spacetime manifold. The vast majority of causal sets, though, are not at all continuum-like, and if we take the discrete description to be fundamental, we must somehow suppress these "bad" sets. I will discuss some recent progress in showing that a very large class of non-manifoldlike sets is very strongly suppressed in the ordinary gravitational path integral, perhaps allowing us to recover the observed continuum structure of spacetime from the quantum theory of a discrete structures.

Quantum Dynamics of Causal Sets: Progress and Challenges

• Sumati Surya (Raman Research Institute)

Room: Valkhofzaal I will give an overview of quantum dynamics in causal set theory. Because of the fundamental (causal) non-locality of causal sets, the dynamics is best described in the language of histories or the path integral formulation. The approach, to date, has been broadly two pronged: the first uses a continuum-inspired partition function and the discrete Einstein Hilbert action while the second uses first principles to construct the decoherence functional within a "growth" paradigm. I will describe recent progress in both and the open questions and challenges that remain.

Q&A for both talks Room: Valkhofzaal

Remarks on Euclidean dS

• Dionysios Anninos (King's College)

Room: Valkhofzaal We explore some properties of de Sitter spacetime, emphasizing the Euclidean perspective, including the path integral over the sphere. We consider the problem in various dimensions.

CDT lessons for Regge gravity and spin foams

• Bianca Dittrich (Perimeter Institute)

Room: Valkhofzaal Spin foams and Regge gravity can be formulated as Lorentzian path integrals. But which configurations should be included in these Lorentzian path integrals, and how should one evaluate these highly oscillatory integrals? Using a simple configuration describing a cosmological spacetime, I will illustrate how these path integrals may be able to address the conformal factor problem and deal with configurations describing topology change.

Talk Lee Smolin

• Lee Smolin (Perimeter Institute)

Room: Valkhofzaal

Q&A for all three talks Room: Valkhofzaal

Loop models on CDTs and height coupled trees.

• Bergfinnur Durhuus (University of Copenhagen)

Room: Valkhofzaal We consider two different kinds of loop models coupled to causal dynamical triangulations, a dense and a dilute one, and describe a mapping onto certain random tree models in which the weights of individual trees depend on their height in addition to their size, in the dilute case. We explain that this height coupling is non-trivial in the sense that it influences the fractal structure of the trees and CDTs.

A spin-off from quantum gravity

• Dario Benedetti (Centre de Physique Théorique, Ecole Polytechnique)

Room: Valkhofzaal Tensor models were introduced in the early 1990s as a generalization of matrix models, generating Feynman diagrams in one-to-one correspondence with higher-dimensional dynamical triangulations. However, there was initially no way to fix the topology of the diagrams, and no way to construct a large-N limit. The latter was only discovered in 2010, leading to a number of analytical results. In particular, the large-N limit of tensor model was shown to be dominated by so-called melonic diagrams, a small subclass of planar diagrams. Unfortunately, from the quantum gravity point of view, so far this has not led to a concrete progress, as the melonic diagrams describe the universality class of branched polymers, already found numerically in the 1990s. Nevertheless, the melonic limit has been revived more recently in the context of the Sachdev-Ye-Kitaev model, and of quantum field theories with the tensor model type of global symmetries. In this talk I will fill in some details of this story, and briefly review some results obtained in the quantum field theory applications of the melonic large-N limit, where such limit provides a useful theoretical tool for constructing and studying a new class of interacting fixed points of the renormalization group.

Q&A for both talks Room: Valkhofzaal

Asymptotic safety as a limit of asymptotic freedom

• Roberto Percacci (SISSA, Trieste)

Room: Valkhofzaal

Renormalization and Running in Higher Derivative Theories

• John Donoghue (University of Massachusetts Amherst)

Room: Valkhofzaal In preparation for a lattice Monte Carlo study, I consider some simpler theories related to Quadratic Gravity and Asymptotic Safety. In particular, I discuss why the logarithmic running of coupling constants is different than that which has been discussed in the literature. In addition, I explore the apparent necessity of a strongly coupled region, independent of the behavior of the running couplings.

Q&A for both talks Room: Valkhofzaal

Should one expect a unique vacuum in Quantum Gravity?

• Max Niedermaier (University of Pittsburgh)

Room: Valkhofzaal The talk examines possible answers to the question raised in functional integral based formulations of Quantum Gravity. These include Lorentzian signature perturbation theory and non-perturbative settings starting from the Euclidean propagation kernel. In the latter framework the "no-boundary" proposal is reexamined in relation to the (non-)normalizability of ground state wave function(s). Finally, noting that even after a complete gauge fixing residual global invariances may survive, their role in triggering vacuum degeneracy is outlined.

U(1)$^3$ quantum gravity – an invitation to all approaches

• Thomas Thiemann (FAU, Erlangen-Nürnberg)

Room: Valkhofzaal Smolin's weak Newton constant limit of 4D Euclidian signature vacuum general relativity, mathematically a consisten U(1)$^3$ deformation of SU(2) quantum gravity, has recently been shown to be quantum integrable, that is, the canonical quantisation programme can be completed. An explicit quantum representation of the Bergmann Komar "group" (the "exponentiation" of the hypersurface deformation "algebra") can be found and the physical Hilbert space, the physical Hamiltonian and the quantum algebra of Dirac observables can be constructed. A cosmological constant can be included and an extension to Lorentzian signature is possible. The model thus appears to be an ideal testing ground for all approaches to quantum gravity -- a "quantum gravity harmonic oscillator". In this talk, these developments, which crucially rest on the non-degeneracy of quantum metrics, will be summarised and possible consequences for actual quantum gravity will be discussed.

Q&A for both talks Room: Valkhofzaal

Some recent geometric ideas in cosmology

• Domenico Giulini (Leibniz University Hanover )

Room: Valkhofzaal

On the affinities between Cosmology and Quantum Gravity

• Mairi Sakellariadou (King's college)

Room: Valkhofzaal I will first highlight the main open questions in cosmology and give some examples of how one could address them in the context of quantum gravity. I will then argue that cosmology, in particular in the gravitational-wave astronomy era, can provide a powerful way of testing quantum gravity.

Q&A for both talks Room: Valkhofzaal

Experimental paradoxes at the gravity-quantum interface

• Markus Aspelmeyer (University of Vienna )

Room: Valkhofzaal

Explorations of non-inertial and analogue gravity vacuum photon production processes with table-top set-ups

• Miles Blencowe (Dartmouth College)

Room: Valkhofzaal An atom defect attached to the surface of a vibrating, micron-scale membrane can experience accelerations comparable to the surface gravity of a neutron star. As one example application, we show how one can feasibly generate and detect photons from the electromagnetic vacuum as a result of the non-inertial membrane motion. In another existing table-top set-up comprising a non-linear electromagnetic transmission line, we show the existence of propagating soliton wave solutions that form analogues of black-white hole horizon pairs, with photons generated from the electromagnetic vacuum in the vicinity of the horizons. As a result, the otherwise stable solitons should evaporate as they propagate along the transmission line; evaluating the soliton evaporation backreaction process fully within quantum field theory (as opposed to semiclassically) is an interesting theory challenge. Such table-top investigations can help shed light on the interplay between gravity and quantum matter/radiation fields under conditions where particle production from vacuum is relevant.

Q&A for both talks Room: Valkhofzaal

Round table discussion Room: Valkhofzaal

Fundamental decoherence from quantum spacetime

• Giulia Gubitosi

Room: Valkhofzaal The emergence of the classical macroscopic world from the microscopic quantum realm is a long-standing open problem, still heavily debated in the physics community and subject to theoretical and experimental research. I will show that quantum properties of spacetime, encoded by noncommutativity at the Planck scale, lead to a generalized time evolution of quantum systems in which pure states can evolve into mixed states. Specifically, a Lindblad equation arises naturally as the evolution equation of quantum systems living in a noncommutative spacetime, where the symmetry generators are deformed and described by nontrivial Hopf algebras. This leads to a fundamental decoherence mechanism by which the density operator of a quantum system asymptotically approaches a maximally mixed state. By analysing the decoherence time for the evolution of a free particle I will also show that that the Planck mass is the maximum allowed mass for elementary quantum systems.

Hamiltonians and quantum gravity: present and future

• Fernando Barbero (IEM-CSIC, Madrid)

Room: Valkhofzaal The canonical quantization of gravity relies on its Hamiltonian formulation in an appropriate phase space. A geometric approach to the Hamiltonian treatment of singular field theories is very useful, especially when the spacetime manifold has boundaries. In the present talk I will quickly review these geometric methods, illustrate how they work with a very quick derivation of the real Ashtekar formulation, and discuss the need to carefully characterize the field spaces used to formulate the theory.

Q&A for both talks Room: Valkhofzaal

Space-time from foliations

• Martin Bojowald (Penn State)

Room: Valkhofzaal A classic result of canonical general relativity, going back to Dirac, shows that general covariance and deformation symmetries of spatial hypersurfaces are equivalent only when the Hamiltonian and diffeomorphism constraints are imposed. A recent mathematical analysis by Blohmann, Schiavina and Weinstein has revealed the appearance of a higher algebraic structure with an L-infinity bracket in hypersurface deformations. These features may have implications for foliation-based approaches to quantum space-time, such as canonical quantum gravity or causal dynamical triangulations.

Geometric actions for gravity

• Glenn Barnich (ULB, Brussels)

Room: Valkhofzaal After reviewing how geometric actions capture the dynamics of asymptotically anti-de Sitter and flat spacetimes in three dimensions, the construction is extended to four dimensions where it yields BMS4 invariant dual field theories. Based on arxiv: 1707.08887, arxiv: 2211.07592

Q&A for both talks Room: Valkhofzaal

Black hole entropy in the causal set approach to quantum gravity

• Fay Dowker (Imperial College)

Room: Valkhofzaal I will review work towards a statistical mechanical account of black hole entropy -- and causal horizon entropy more generally -- within causal set theory.

Linear local gauge invariant observables: construction and applications

• Igor Khavkine (Institute of Mathematics, Czech Academy of Sciences)

Room: Valkhofzaal The Killing operator $K_{ab}[v]=\nabla_a v_b + \nabla_b v_a$ is the generator of gauge symmetries (linearized diffeomorphisms) $h_{ab}\mapsto h_{ab} + K_{ab}[v]$ in linearized gravity. A linear local gauge-invariant observable is a differential operator $I[h]$ such that $I[K[v]] = 0$ for any gauge parameter field $v_a$. A set $\{I_i[h]\}$ of such observables is complete if the simultaneous conditions $I_i[h] = 0$ are sufficient to conclude that the argument is locally a pure gauge mode, $h_{ab} = K_{ab}[v]$. The explicit knowledge of a complete set of local gauge invariant observables has multiple applications from the points of view of both physics and geometry, whenever a precise separation of physical and gauge degrees of freedom is required. I will sketch some recent progress on constructing complete sets of such observables on spacetimes of sub-maximal symmetry (like cosmologies and black holes) and applications thereof.

Q&A for both talks Room: Valkhofzaal

Why quantum gravity, and CDT in particular, may be expected to be classical.

• Gerard 't Hooft (Utrecht University)

Room: Valkhofzaal Black holes tell us that, at the Planck scale, information in spacetime should be coarse-grained. Carefully studying the foundations of quantum mechanics, one also hits upon coarse grained structures, but they are classical. Quantum behavior automatically comes about when taking the continuum limit. This suggests that the logic applied in CDT should also be classical logic. This may remove some of the quantum mysteriousness of General Relativity, but of course it raises other questions, of which some will be addressed.

Q&A Room: Valkhofzaal

Closing words Room: Valkhofzaal