Quantum Gravity

Instead of formulating the state space of a quantum field theory over a single big Hilbert space, it has been proposed by Jerzy Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. I will discuss the physical motivations for this approach and explain how it can be implemented in the context of LQG. While the resulting state space forms a natural extension of the Ashtekar-Lewandowski Hilbert space, it treats position and momentum variables on equal footing. This paves the way for the construction of semi-classical states beyond fixed graph level, and eventually for the derivation of LQC from full LQG.

I offer a personal perspective on the causal dynamical triangulations approach to the construction of quantum theories of gravity. After briefly introducing the approach's formalism and results, I illuminate this perspective with 3+1 vignettes of recent and ongoing research. Specifically, I review attempts to locate an ultraviolet fixed point through renormalization group analyses; I report measurements of the homogeneity of the approach's quantum geometries; I discuss efforts to determine the large scale effective action in the case of 2+1 dimensions; and I suggest a speculative possibility for reviving the Euclidean dynamical triangulations approach.

A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new non-geometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Barbero-Immirzi parameter.

We will discuss our work on (1) the global food crisis and the implications for how we can address hunger and social unrest around the world, (2) the financial crisis and the implications for the role of regulation in economic market stability, and (3) the Ebola epidemic and the vulnerability of global civilization to pandemics. 

I will review recent work on tensorial group field theories (TGFTs). The renormalization methods being developed in this context provide more and more control over their field-theoretic structures, and for models which increasingly resemble loop quantum gravity. Perhaps surprisingly, some of these models are asymptotically free and can therefore be made sense of at arbitrary values of the (abstract) scale with respect to which they are organized. They define in this sense UV complete quantum field theories. I will focus on TGFTs with gauge invariance condition, which allow for such a behavior but also for more complicated scenarii involving non-trivial fixed points of the renormalization group flow. I will finally comment on the physical relevance of this notion of UV completion.

It is by now well established that black holes emit a thermal radiation and undergo an evaporation process. The original Hawking evaporation scenario, based on quantum fields on a classical background geometry, has been vastly extended and improved, in order to take into account in particular the backreaction of the radiation on the geometry. This can be done for example in a semiclassical setup, where the Einstein equations are sourced by an effective stress energy tensor. In two-dimensional models, this is a powerful method since the conformal anomaly enables one to reconstruct unambiguously the full effective stress energy tensor, or the corresponding effective matter action. However, attempts to generalize this method in four dimensions have been so far partly unsuccessful. In this talk we will review the difficulties that arise in attempts to constructing the effective action for matter fields coupled to a dilaton, and focus on a potential way out of the problem. This could lead to a new expression for the effective stress energy tensor on a black hole geometry, and to progress in the the study of backreaction in four-dimensional spherically symmetric models.

I present a proposal for a worldline action for discretized gravity with the same field content as loop quantum gravity. The proposal is defined through its action, which is a one-dimensional integral over the edges of the discretization. Every edge carries a finite-dimensional phase space, and the evolution equations are generated by a Hamiltonian, which is a sum over the constraints of the theory. I will explain the relevance of the model, and close with possible relations to other approaches of quantum gravity, including: relative locality, causal sets and twistor theory.