Quantum Gravity

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.

When performing the gravitational path integral, multiple saddles can contribute to a given computation. In black hole thermodynamics, one encounters infinitely many critical points of the action, most of which are complex. Surprisingly, the sum over these saddles diverges in spacetime dimensions greater than three, and the on-shell action is not even bounded from below. Starting from the Lorentzian gravitational path integral, we show that only a finite number of saddles actually contribute. Interestingly, as the temperature decreases, the number of relevant saddles increases, reproducing known results from JT gravity coupled to gauge fields in the extremal limit. We also discuss the implications of this approach for the computation of supersymmetric indices.

In this talk, I will describe recent developments in our understanding of edge modes associated to subregions in gauge theories, leveraging their realization as reference frames. I will begin with the picture in classical Maxwell theory, where I will introduce the concept of subregional Goldstone mode as a relational observable parametrizing the corner symmetry group. With this as a guiding principle, I will then move on to non-Abelian lattice gauge theory, where we can carry out the construction directly at the quantum level. I will characterize a novel hierarchy of relational subregional algebras, which encompasses the so-called electric and magnetic center algebras usually considered in the literature, for which we provide a new general definition. This leads to corresponding entropy hierarchies. Interestingly, some of the relational algebras can be factors, and so the physical Hilbert space factorizes. Except in the Abelian case, the subregional Goldstone mode is generically only defined on a subspace of the Hilbert space, stemming from the incompleteness of certain edge mode frames. I will conclude with on-going efforts to have a quantum description of edge modes in the continuum, employing algebraic QFT methods. An overarching theme will be the relation between the subregional Goldstone mode and the asymptotic soft sector of the theory. 

Defining thermodynamic ensembles for gravitational systems is tied to specifying boundary conditions. In this talk I'll first briefly review how introducing a Dirichlet timelike boundary clarifies thermodynamics of de Sitter space. Then I'll discuss geometries subjected to conformal boundary conditions, where the conformal class of the boundary metric and the trace of the extrinsic curvature K are held fixed. In the high temperature limit the series of subextensive terms in the free energy are compared to predictions from thermal effective field theory, and we observe agreement in all considered cases. Ensembles with negative K include solutions with cosmic-type horizons, where the system boundary is smaller than the horizon. In some regions of parameter space, these solutions are the dominant phase and are necessary for consistency with thermal effective field theory.

Most physical theories assume that spacetime is four dimensional, a claim strongly supported by high precision accelerator and cosmological measurements. It is also well known that at the Planck scale our quantum theories, and perhaps physics itself, break down. This raises a natural question: what happens to spacetime at the smallest scales, where quantum fluctuations may alter the familiar four dimensional structure? What is the dimension of quantum spacetime? How should we understand topology in this regime, and can matter and spacetime topology be defined independently? My talk will present possible answers to these questions through the lens of Causal Dynamical Triangulations.