Quantum Gravity

In the search for a consistent and renormalizable quantum theory of gravity, a conservative possibility is that gravity admits a field-theoretic description valid up to arbitrarily high energies. This amounts to going beyond the perturbative non-renormalizability of general relativity and it can be achieved following different strategies. One is to abandon Lorentz invariance as a fundamental symmetry to gain power-counting renormalizability, as in Hořava Gravity. In Asymptotically Safe Gravity, ultraviolet completeness instead arises from a non-perturbative renormalization group fixed point, preserving spacetime symmetries. In both cases, the peculiar UV structure of the theory reflects in its low-energy description, with a particular imprint on black hole physics. In this talk, I will explore these two scenarios as UV description of gravity. I will focus both on their high-energy description, reviewing some recent developments, and on the possible low-energy physics stemming from each assumption.

Gibbons and Hawking proposed that the Euclidean gravity path integral with periodic boundary conditions in time computes the thermal partition sum of gravity. As a corollary, they argued that a derivative of the associated free energy with respect to the Euclidean time period computes gravitational entropy. Why is this interpretation correct?  That is, why does this path integral compute a trace over the Hilbert space of quantum gravity?   I will show that the quantity computed by the Gibbons-Hawking path integral is equal to an a priori different object -- an explicit thermal trace over the Hilbert space spanned by states produced by the Euclidean gravity path integral. I will explain that this follows if the Hilbert space with two boundaries factorizes into a product of two single boundary Hilbert spaces.  To show the latter I will develop a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. I will use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space, from which our main result will follow.

Suppose our universe really had a huge cosmological constant.  What would this mean observationally?  For a homogeneous universe the answer is clear, but if the universe is inhomogeneous at the Planck scale the question becomes more subtle.  At the level of initial data, $\Lambda$ can be "hidden" in spacetime foam, rapidly expanding and contracting regions that coexist and give an average expansion near zero.  Classically, such data develop singularities, and we need a quantum description of their evolution.  I describe results from a spherically symmetric midisuperspace model in which the wave function can become "trapped" for long periods in regions in which the average expansion remains small, effectively hiding a large cosmological constant.

Higher-curvature gravity can offer UV completions of GR, but generically suffers from 4th-order propagating degrees of freedom often spoiling unitarity, e.g. Stelle gravity. Recently it was noticed that “Einsteinian gravities” allow for higher curvature interactions match Einstein’s spectrum at the linearised level, avoiding the dangerous 4th-order propagating degrees of freedom. We investigate the renormalisation group flow of Einstein cubic gravity couplings and identify the entire phase diagram of the theory, showing that Einstein cubic gravity remains ghost-free in the quantum regime. To tackle questions of unitarity and causality directly, we make a Lorentzian computation of the asymptotically safe graviton propagators of the transverse-traceless and scalar mode. We showed that beyond the requirement of using a causality-preserving regulator, such as Callan-Symanzik, setting up differential equations for coupled spectral functions must satisfy additional constraints related to diffeomorphism and BRST symmetry. We found three avenues to solve the coupled system of running Kallen-Lehmann spectral representations, leading to 1-loop exact spectral functions which are compatible with causality and unitarity. Furthermore, they provide the first direct asymptotically safe predictions to the full quantum propagators, the corresponding Weyl-tensor and Ricci-scalar form factors in the quantum effective action.

We study subregion algebras in classical and perturbative quantum gravity on half-spaces of event horizons. We construct half-sided supertranslation generators by extending subregion phase spaces of the event horizon to include doubled pairs of edge modes obtained from splitting the horizon. These edge modes carry a corner symplectic form that gives rise to canonical generators of half-sided boosts and translations, the former of which is the area operator at the corner while the latter corresponds to null time evolution along the horizon. The charges act nontrivially on gravitationally dressed bulk observables, such that subalgebras take the form of a crossed product by the associated automorphism group. Quantizing the extended phase space after linearizing around a black hole, we obtain for each cut a Type II$_{\infty}$ von Neumann algebra whose entropy coincides with the generalized entropy of that cut. The nesting property of the resulting one-parameter family of subalgebras implies a generalized second law for linearized perturbations of Killing horizons. Finally, we use gravitational half-sided modular inclusion algebras to prove quantum focusing along Killing horizons in the perturbative quantum gravity regime.

Small naked singularities—those not shielded by a macroscopic event horizon—are ubiquitous in classical General Relativity. Their existence constitutes apparent violations of the weak cosmic censorship conjecture, which asserts that physically reasonable solutions should appear regular to asymptotic observers. In this talk, we will show how the inclusion of stringy and quantum effects resolves these pathologies by uplifting naked singularities into fully regular configurations. Focusing on critical gravitational collapse as a concrete example, we demonstrate that a proper quantum treatment replaces naked singularity formation with black hole formation. This suggests that cosmic censorship is not fundamentally a property of classical General Relativity, but rather emerges only once quantum gravitational effects are taken into account.

In this talk, I will argue that the universal structure of the corner algebra offers a new perspective on quantum gravity, in which the representation theory of this algebra plays a role as fundamental as that of the Poincaré algebra in quantum field theory. I will discuss the representation theory of the (quantum) universal and extended corner symmetries in a simplified model of spherically symmetric spacetimes, where the corner reduces to a point and the algebra correspondingly simplifies. Furthermore, I will propose a purely algebraic procedure for gluing regions in the quantum theory, compute the entanglement entropy, and derive the entropy–area law for a class of specific coherent states.

In this talk, we will provide an overview of recent developments in the quantization of Cylindrically symmetric spacetimes, which contain the Einstein-Rosen gravitational waves. This class of solutions leads to an integrable field theory, and its phase space can be expressed directly in terms of initial data living on a null generator. The corresponding Poisson algebra appears in the double null sheet formulation of full 3+1 gravity (Reisenberger, 2007), as essentially a Poisson subalgebra on each null generator. This suggests that the algebraic quantization introduced by Korotkin-Samtleben in the context of cylindrically symmetric gravity is relevant for the search for the full quantum theory. We will present some results concerning this quantum algebra, where two Wick-type algebraic structures emerge. Finally, we will discus the known quantization of the Einstein-Rosen waves with one polarization, due to Ashtekar-Pierri, as a subsector of the general two polarizations case.

We study thermodynamics of spherically-symmetric spacetime with the aim of exploring spacetime entropy as an adiabatic invariant. We first describe the geometry and dynamics in terms of a local frame adapted to spherical foliations and find a geometro-hydrodynamic interpretation: the spacetime can be viewed as the worldvolume of a concentric stack of "gravitational bubbles", spherical collective modes with the Misner-Sharp energy density and a geometric pressure. We then introduce a notion of work and heat, and investigate the covariant phase space of a thermodynamic action corresponding to the adiabatic boundary condition. Identifying the phase space with the thermodynamic state space, these should provide the foundation for the spacetime thermodynamics. As an example, we apply this to the apparent horizon and employ Caratheodory’s idea, to derive the entropy of the dynamical horizon as an adiabatic-invariant Hamiltonian. This agrees with the Bekenstein-Hawking formula for the surface area of the apparent horizon, where a dynamical version of Hawking temperature appears. [arXiv: 2601.03077 + to appear]

Carrying the insights of conditional probability to the quantum realm is notoriously difficult due to the non-commutative nature of quantum observables. Nevertheless, conditional expectations on C* and von Neumann algebras have played a significant role in the development of quantum information theory, and especially the study of quantum error correction. In quantum gravity, it has been suggested that conditional expectations may be used to implement the holographic map algebraically, with quantum error correction underlying the emergence of spacetime through the generalized entropy formula. However, the requirements for exact error correction are almost certainly too strong for realistic theories of quantum gravity. In this talk, we provide an overview of the multifaceted nature of quantum conditional probability by exploring different non-commutative generalizations of conditional expectations which meet the demands of non-exact error correction. We then exemplify the utility of these tools through two examples. First, we demonstrate how operator valued weights can be used to classify the possible symmetries (including non-invertible symmetries) of a quantum system. Then, we introduce a generalization of Connes’ spatial theory leading to a fully non-commutative form of Bayes' law. This allows for an exact quantification of the information gap occurring in the data processing inequality for arbitrary quantum channels. When applied to algebraic inclusions, this further provides an approach to factorizing the entropy of states into a sum of terms including an emergent area operator that is fully non-commutative rather than central. 

Spacetime fluctuations can invalidate usual notions of distance, time, and even what it means to perform an experiment. This raises a simple question: when spacetime fluctuates, how do we describe what happens? Few detailed ​answers exist, even in the low-energy effective field theory of quantum gravity. In this talk, we present a study of geometric and detector observables in perturbative quantum gravity. Geometric observables—elapsed proper time, proper distance, area, and Shapiro time delay—can be defined in relation to observer worldlines. Proper time observables capture quantum gravity effects in interferometers, leading to predictions for experiments that probe the interface between quantum mechanics and gravity. Several geometric observables display a quantum version of memory. Realistic detector observables—modelled by local operators inserted along worldlines—describe measurements more directly. We compute correlators of worldline-dressed scalars at tree level with an external on-shell graviton. The worldline dressing is hardly innocuous and can, in fact, induce enormous corrections. Gravitational effects can either open or close light cones, as captured by the commutator of dressed scalars. Finally, we discuss the broader landscape of observables now within closer reach in effective field theory and holography.

Whether quantum gravitational effects can be enhanced beyond the Planck scale is an important question for testing quantum gravity. In this talk, I will present how the fluid/gravity correspondence provides insight into the enhancement of quantum gravity fluctuations in a finite causal diamond. I will begin by reviewing the fluid/gravity correspondence in Rindler space. Based on this setup, I will show a dual fluid description of shockwave geometry using the Petrov classification. Then, I will discuss ongoing progress toward understanding connections with Carrollian fluids living on the boundary of causal diamonds. I will conclude by clarifying the assumptions under which an observable scale could emerge.