Quantum Gravity

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.

In this talk, we analyze detector operators that measure energy to the power ∆-2 at null infinity in Einstein gravity. These operators transform as conformal primaries on the celestial sphere and provide a natural basis for describing energy-flux observables in scattering processes. Using the collinear factorization of scattering amplitudes, we derive the universal leading structure of the operator product expansion (OPE). A key consequence of our analysis is the precise identification of the ∆=2 detector, the number operator. Exploiting the fact that soft charges generate symmetries of the S-matrix, we demonstrate that the number of particles is entirely determined by the product of two supertranslation currents. This work establishes a direct link between detector observables and the soft sector of celestial holography. Analogous conclusions hold for Yang–Mills theory. 

We explicitly construct the density matrix associated to the vacuum state of a large spherically symmetric causal diamond in four-dimensional asymptotically flat gravity. We achieve this using the soft effective action, which characterizes the low-energy gravitational degrees of freedom that arise in the long-distance limit of the Einstein-Hilbert action and consists of both the soft graviton mode and the Goldstone mode arising from the spontaneous breaking of supertranslation symmetry. Once we have the density matrix, we straightforwardly compute the mean and variance of the modular Hamiltonian and in particular show that the variance obeys an area law.

Elementary quantum reference frames (QRFs) such as clocks have recently led to surprising insights into quantum gravity. But far richer structures should emerge once we consider more full-fledged gravitational QRFs, i.e. quantum coordinate systems. A complete theory of such objects remains elusive, largely due to the subtleties in quantizing diffeomorphism symmetry. Null surfaces provide an ideal simplified setting to explore the properties of quantum coordinates. In this talk, I will show how one may form a useful QRF out of the area/spin 0 degrees of freedom on each light ray: the quantum dressing time. This construction permits relational observables and frame reorientations within an algebraic structure generalizing the crossed product, and consistent with established QRF approaches such as the perspective-neutral formalism. Along the way, I will discuss how diffeomorphism anomalies can be cancelled by the introduction of a suitable classical counterterm; I will describe some implications of the fact that QRFs made from fields (such as the quantum dressing time) must be Kähler-quantised; and I will comment on the consequences of our construction for gravitational entropies. Based on 2510.26589 and WIP with Laurent Freidel.

Motivated by recent advances in "non-Lorentzian" physics, I will revisit the light-cone formulation of QFT, which has played a central role in the quantization of gauge theories. Much of its success can be traced to the presence of an underlying non-relativistic (Galilean) structure within the light-cone Poincaré algebra. I will show that light-cone Minkowski space belongs to a broader class of non-Lorentzian geometries, whose isometry algebra accommodates several interesting kinematical subalgebras—particularly of the Galilean and Carrollian types. These kinematical Lie algebras encode the symmetry transformations that govern spacetime kinematics and the evolution of physical systems. Finally, I will discuss certain aspects of light-cone field theories, emphasizing their connection to the hypersurface deformation algebra associated with Carrollian geometries, as well as their possible implications.

The good books on GR agree on certain aspects of the theory that we could consider to be its “core” features. Beyond the core, however, we do not know exactly what GR should allow or not allow physically. For example, should we consider spacetimes with closed causal loops as part of physical GR or not? Are spacetimes with certain types of boundaries or singularities part of GR?  Most people expect that the answer to these sorts of questions will be answered by quantum gravity when we have it.  We can start to address them within different quantum gravity approaches even at their current partial state of their development. Within the framework of the path integral for quantum gravity and a Feynmanian heuristic for the recovery of the classical approximation, I will sketch out how answers may arise. I will use the example of causal set quantum gravity but I suggest that the ideas are applicable to other path integral approaches.

The first part of the talk will briefly discuss the tasks that need to be accomplished in order to formulate such open quantum models in the context of quantum gravity, as well as the challenges involved. As a first step in this direction, a QFT model in the context of linearised gravity is presented, which is formulated in Ashtekar-Barbero variables and then Fock-quantised with a special choice of so-called geometrical clocks as a reference frame. The corresponding master equation and its renormalisation are discussed. Inspired by this QFT model, the second part of the talk presents an application of a quantum mechanical toy model in the context of neutrino oscillations and compares it with existing phenomenological models.

Models for gravitationally induced decoherence can be formulated within the framework of open quantum systems, in which gravity is chosen as the environment and quantised together with the system under consideration. The effective dynamics of the system under the influence of the environment are encoded in the so-called master equation. Existing phenomenological models often take the Lindblad equation as the starting point for the master equation, while from the perspective of quantum gravity approaches, an underlying microscopic model from which a field-theoretical master equation can be derived seems to be the more accessible approach, which also makes it possible to establish a connection between microscopic and phenomenological models.