This series consists of talks in the area of Quantum Gravity.
The computation of transition amplitudes in Loop Quantum Gravity is still a hard task, especially without resorting to large-spins approximations. In Marseille we are actively developing a C library (sl2cfoam) to compute Lorentzian EPRL amplitudes with many vertices. We have already applied this tool to obtain interesting results in spinfoam cosmology and on the so-called flatness problem of spinfoam models.
Since the seminal work of Penrose, it has been understood that conformal compactifications (or "asymptotic simplicity") is the geometrical framework underlying Bondi-Sachs' description of asymptotically flat space-times as an asymptotic expansion. From this point of view the asymptotic boundary, a.k.a "null-infinity", naturally is a conformal null (i.e degenerate) manifold. In particular, "Weyl rescaling" of null-infinity should be understood as gauge transformations.
Using a definition of bulk diff-invariant observables, we go into the bulk of 2d Jackiw-Teitelboim gravity. By mapping the computation to a Schwarzian path integral, we study exact bulk correlation functions and discuss their physical implications. We describe how the black hole thermal atmosphere gets modified by quantum gravitational corrections. Finally, we will discuss how higher topological effects further modify the spectral density and detector response in the Unruh heat bath.
We introduce a new technique to study the critical point equations of the eprl model. We show that it correctly reproduces the 4-simplex asymptotics, and how to apply it to an arbitrary vertex. We find that for general vertices, the asymptotics can be linked to a Regge action for polytopes, but contain also more general geometries, called conformal twisted geometries. We present explicit examples including the hypercube, and discuss implications.
The full theory of LQG presents enormous challenge to create physical computable models. In this talk we will present the new modern version of Quantum Reduced Loop Gravity. We will show that this framework provide an arena to study the full LQG in a certain limit, where the quantum computations are possible. We will analyze all the major step necessary to build this framework, how is connected with the full theory, its mathematical consistency and the physical intuition behind It.
Quantum-reduced loop gravity is a model of loop quantum gravity, whose characteristic feature is the considerable simplicity of its kinematical structure in comparison with that of full loop quantum gravity. The model therefore provides an accessible testing ground for probing the physical implications of loop quantum gravity. In my talk I will give a brief introduction to quantum-reduced loop gravity, and examine the relation between the quantum-reduced model and full loop quantum gravity.
The covariant (spinfoam) formulation of loop gravity is a tentative physical quantum theory of gravity with well defined transition amplitudes. I give my current understanding of the state of the art in this research direction, the issues that are open and need to be explored, and the current attempts to use the theory to compute quantum effects in the early universe and in black hole physics.
It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries (Lorentz symmetries) parametrized by the value of the cosmological constant. They appear as some kind of regularization either through the quantization of the Chern-Simons formulation (Fock-Rosly formulation/combinatorial quantization, path integral quantization) or the state sum approach (Turaev-Viro model). Such deformation might be perplexing from a classical picture since the action is defined in terms of plain/undeformed gauge symmetry.
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.