Quantum Gravity

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.

The original spinfoam amplitude, Ponzano-Regge, has two properties in seeming contradiction: (1.) It can be written as an integral of a product of Dirac delta functions imposing that holonomies be exactly flat, and (2.) In its original sum-over-spins form, its leading order large spin asymptotics consist in Regge calculus, modified to include an additional local discrete orientation variable for each tetrahedron, which, when fixed inhomogeneously, leads to critical point equations for the edge lengths which do not necessarily imply flatness, but allow spikes. Of course, this apparent contradiction between flatness and spikes appears only for triangulations with bubbles, for which both of these formulations of the model are divergent and ill-defined anyway, and this may be the resolution of the paradox. However, we explore the possibility of another resolution of this paradox which may also have relevance for the semiclassical regime of 4D spinfoams, in which a similar sum over local orientations appears.

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.