I can't say that it will be relevant to the topic of the talk (Continuum Limit and Renormalization) but this recent paper by Freidel is pretty amazing. "Local holography" is a whole new approach to QG. Spatial locations (neighborhoods of points) are surrounded by TUBULAR SCREENS. There is an interesting rationale motivating this:
http://arxiv.org/abs/1312.1538
Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
Laurent Freidel
(Submitted on 5 Dec 2013)
We study the properties of gravitational system in finite regions bounded by gravitational screens. We present the detail construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy and viscous stress tensor, while the conservations are analogs of non-equilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and non-equilibrium thermodynamics.
41 pages, 3 figures
==try thinking through this motivation, quote page 1==
Unlike any other interactions, gravity is fundamentally holographic. This fundamental property of Einstein gravity manifests itself more clearly when one tries to define a notion of energy for a gravitational system. It is well known that no local covariant notion of energy can be given in general relativity. The physical reason can be tracked to the equivalence principle. Illustrated in a heuristic manner, a free falling point-like particle does not feel any gravitational field, so no gravitational energy density can be identified at spacetime points. A more radical way to witness the holographic nature of gravity, comes from the fact that the Hamiltonian of general relativity coupled to any matter fields, exactly vanishes for any physical configuration of the fields. If one asks what is the total energy of a closed gravitational system with no boundary, the answer is that it is zero for any physical configurations. This is a mathematical consequence of diffeomorphism invariance. It naively implies that the gravitational energy density vanish.
A proper way to accommodate this, is to recognize that a notion of energy can only be given once we introduce a bounded region of space together with a time evolution for the boundary of this region. The time evolution of this boundary span a timelike world tube equipped with a time foliation. We will call such boundaries equipped with a timelike foliation, gravitational screens. They will be the subject of our study which focuses on what happen to a gravitational system in a finite bounded region. In the presence of gravity, the total energy of the region inside the screen comes purely from a boundary screen contribution and the bulk contribution vanishes. In that sense, energy cannot be localized but it can be quasi-localized, i-e expressed as a local surface integral on the screen.
==endquote==
