This series consists of talks in the area of Quantum Gravity.
In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand the Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes.
Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem:
(C) Which gauge invariant degrees of freedom are associated to a region with boundaries?
Quantizing 4D geometries leads to discrete area spectra. Such discrete area spectra are also suggested by the holographic principle and entropy counting for black holes.
In order to solve the problem of time in quantum gravity, various approaches to a relational quantum dynamics have been proposed. In this talk, I will exploit quantum reduction maps to illustrate a previously unknown equivalence between three of the well-known ones: (1) relational observables in the clock-neutral picture of Dirac quantization, (2) Page and Wootters’ (PW) Schrödinger picture formalism, and (3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity.
In this talk, we present a new outlook on canonical quantum gravity and its coupling to matter.
We will review the gravitational formula for fine grained entropy. We will discuss how it applies to an evaporating black hole and how we can compute the entropy of Hawking radiation.
In this talk I will discuss some recent results on boundary degrees of freedom (or edge modes), and their description via an extended phase space structure containing extra boundary fields. Motivated by a slight modification of the covariant phase space formalism, I will show how the use of a boundary Lagrangian enables to include the edge modes in the phase space and to obtain their boundary dynamics. This will be illustrated on the example of Maxwell theory, where in addition the edge modes can be understood as contributing to entanglement entropy.
Our earlier findings indicate the violation of the 'volume simplicity' constraint in the current Spinfoam models (EPRL-FK-KKL). This result, and related problems in LQG, promted to revisit the metric/vielbein degrees of freedom in the classical Einstein-Cartan gravity. Notably, I address in detail what constitutes a 'geometry' and its 'group of motions' in such Poincare gauge theory. In a differential geometric scheme that I put forward the local translations are not broken but exact, and their relation to diffeomorphism transformations is clarified.
In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory.