Corner Symmetry and Quantum Geometry - Freidel, Laurent; Geiller, Marc; Wieland, Wolfgang (Handbook of Quantum Gravity, 2023)
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called corners. The presence of non-trivial corner symmetries associated with any entangling cut provides stringent constraints on the theory’s mathematical structure and a guide through quantization. This report reviews new and recent results for non-perturbative quantum gravity, which are natural consequences of this structure. First, we establish that the corner symmetry derived from the gauge principle encodes quantum entanglement across internal boundaries. We also explain how the quantum representation of the corner symmetry algebra provides us with a notion of quantum geometry. We then focus our discussion on the first-order formulation of gravity and show how many results obtained in the continuum connect naturally with the previous results in loop quantum gravity. In particular, we show that it is possible to get, purely from quantization and without discretization, an area operator with discrete spectrum, which is covariant under local Lorentz symmetry. We emphasize that while loop gravity correctly captures some of the gravitational quantum numbers, it does not capture all of them, which points toward important directions for future developments. Finally, we discuss the understanding of the gravitational dynamics along null surfaces as a conservation of symmetry charges associated with a Carrollian fluid.<br

Evidence for Planck luminosity bound in quantum gravity - Wieland, Wolfgang (Classical and Quantum Gravity, 2025)
Recently, we introduced a non-perturbative quantization of impulsive gravitational null initial data. In this note, we investigate an immediate physical implication of the model. One of the quantum numbers is the total luminosity carried to infinity. We show that a transition happens when the luminosity reaches the Planck power LP. Below LP, the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous. A physical state that lies in the continuous spectrum consists of a superposition of kinematical states in which the shear is unbounded from above. We argue that such states are unphysical because they contain caustics that are in conflict with the falloff conditions at asymptotic infinity.
CRIS-Team Scopus Importer:2025-03-14
Keywords: asymptotic structure; gravitational waves; maximum luminosity; Planck luminosity; quantum gravity

Simplicial graviton from selfdual Ashtekar variables - Wieland, Wolfgang (Classical and Quantum Gravity, 2024)
In perturbative gravity, it is straight-forward to characterize the two local degrees of freedom of the gravitational field in terms of a mode expansion of the linearized perturbation. In the non-perturbative regime, we are in a more difficult position. It is not at all obvious how to construct Dirac observables that can separate the gauge orbits. Standard procedures rely on asymptotic boundary conditions or formal Taylor expansions of relational observables. In this paper, we lay out a new non-perturbative lattice approach to tackle the problem in terms of Ashtekar’s self-dual formulation. Starting from a simplicial decomposition of space, we introduce a local kinematical phase space at the lattice sites. At each lattice site, we introduce a set of constraints that replace the generators of the hypersurface deformation algebra in the continuum. We show that the discretized constraints close under the Poisson bracket. The resulting reduced phase space describes two complex physical degrees of freedom representing the two radiative modes at the discretized level. The paper concludes with a discussion of the key open problems ahead and the implications for quantum gravity.
CRIS-Team Scopus Importer:2024-02-02
Keywords: Hamiltonian formalism of general relativity; lattice methods; quantum gravity; selfdual gravity; spinfoams and loop quantum gravity