Quantum Gravity

Numerical methods are powerful tools for advancing our understanding of quantum gravity. In this talk, I will introduce two complementary numerical approaches. The first focuses on solving nonlinear partial differential equations that arise in Loop Quantum Gravity (LQG)-inspired effective models. This framework enables us to investigate the formation and evolution of shock waves in spherically symmetric gravitational collapse. The second approach involves the use of complex critical points, Lefschetz thimble techniques, and the Metropolis Monte Carlo algorithm to study the Lorentzian path integral in Spinfoam models and Quantum Regge Calculus. These methods offer new insights into quantum cosmology and black-to-white hole transitions.

Einstein's theory admits interesting limits with different causal structures obtained by letting the speed of light go to infinity (Galilean or "non-relativistic" limit) or to zero (Carrollian, sometimes called "ultrarelativistic", limit). The Carroll limit turns out to be relevant near spacelike (cosmological) singularities, and particularly so when p-form gauge fields are coupled to gravity as in the context of extended supergravities. The resulting differential equations possess a remarkable interpretation in terms of infinite-dimensional Kac-Moody algebras. The talk will review various aspects of Carroll invariant theories, of the Belinski-Khalatnikov-Lifshitz analysis of spacelike singularities and of the related symmetries.

Discrepancies between Lorentzian and Euclidean calculations of quantum corrections to de Sitter horizon thermodynamics revealed the existence of ‘edge’ degrees of freedom on the horizon. In this talk, I will review these calculations and present updates on understanding the physics of such edge modes in both gauge theories and (higher-spin) gravity. For Einstein gravity, I will discuss a plausible interpretation involving an embedded spherical brane. Finally, I will comment on how these ideas extend to more general black hole spacetimes.

It has been conjectured that the gravitational interaction may arise as an entropic force rather than as a result of virtual quanta exchange of a fundamental field. In this talk I will present a set of microscopic quantum models which realize this idea in detail. I will describe a simple mechanism by which Newton’s law of gravity arises from the extremization of the free energy of a collection of qubits. I will show both a local and non-local model version of the construction and discuss how to distinguish these entropic models from ordinary perturbative quantum gravity using existing observations and near term experiments. Based on 2502.17575 with Daniel Carney, Thilo Scharnhorst, Roshni Singh and Jacob M. Taylor.

In this talk I will discuss the energy probability density function of an evaporating near-extremal charged black hole. At sufficiently low energies, such black holes experience large quantum metric fluctuations in the $AdS_{2}$ throat which are governed by a Schwarzian action. These fluctuations modify Hawking evaporation rates, and therefore also affect how the black hole state evolves over time. In previous work on Schwarzian-corrected Hawking radiation, the black hole was taken to be in the microcanonical or canonical ensemble [arXiv:2411.03447]. However, we find that an initially fixed-energy or fixed-temperature state does not remain so in the regime where Schwarzian corrections are important. We consider three decay channels: the emission of massless scalars, photons, and entangled pairs of photons in angular momentum singlet states. In each of the three cases, we find that in the very low energy, quantum dominated regime, the probability distribution of the black hole energy level occupation tends toward a particular attractor function that effectively depends on only one combination of time and energy. This function is independent of the initial state and gives new predictions for the energy fluxes and Hawking emission spectra of near-extremal charged black holes.

I discuss work in progress on the no-boundary state of the universe in quantum cosmology, emphasizing the key role played by the inclusion of an observer in obtaining a reasonable no-boundary state. For concreteness we focus on a 2d toy model, namely dS JT gravity. This model has avatars of important issues with the wavefunction of the universe in inflationary models. The issues are that the wavefunction predicts a small universe (whereas our universe is rather large), and that it is not normalizable. I show that the non-normalizability is resolved by promoting dS JT gravity to sine dilaton gravity, a type of UV completion of dS JT gravity of which I discuss the cosmological interpretation. I then argue that the issue of predicting a small universe (in this toy model) is resolved by including an observer in the theory. With the observer, the leading contribution is a bra-ket wormhole. The observer's no boundary state is a (maximally mixed) identity matrix, and thus prefers neither small nor large universes.

Local subsystems play a fundamental role in theoretical physics, but they are usually defined in terms of background spacetime structures, in particular a Lorentzian metric. In gravity there are no such structures and the metric becomes dynamical. I will argue that nevertheless subsystems can be constructed in relation to other degrees of freedom, subject to the requirement that those variables reside within the subsystem itself. In operational terms an observer located within the system should be able to determine its edge by taking measurements within that region only. Within the context of classical field theory, I will demonstrate that this guarantees that the observables describing the system constitute a closed Poisson algebra. I'll discuss some examples, explain how surface charges generating subsystem symmetries, including the Bekenstein-Hawking area entropy, are incorporated, and make some remarks about how this can be extended to a fully quantum treatment within the framework of deformation quantization.

Many aspects of classical AdS/CFT can be understood from the point of view of group theory. In this talk, I will argue that applying the same philosophy can provide us with some powerful insights regarding the construction of its flat counterpart, dubbed flat holography. The basic setup will be a massless gauge field of arbitrary (integer) spin propagating on Minkowski spacetime of any dimensions. An asymptotic analysis will reveal the data composing the solution space, as well as the asymptotic symmetries acting on the latter. I will show how part of this solution space can be understood in terms of unitary irreducible representations of the Lorentz group, seen as the group of conformal transformations of the celestial sphere. This interpretation allows us to capture some universal aspects of field theories in Minkowski space-time within the framework of celestial holography, while we will see that the other parts of the solution space have a more natural Carrollian interpretation.