Quantum Gravity

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation could be described by a unitary evolution without the problems encountered by standard remnant scenarios or the schemes where information is assumed to come out with the radiation while semiclassical evaporation (firewalls and complementarity). I point out the possibility that the final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler) which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time.

A renormalization group transformation implements a scale transformation while resetting the UV cut-off, so that the theories before and after the RG transformation contain the same degrees of freedom, but with a modified action. In Wilson's original proposal, the cut-off is reset by integrating out the degrees of freedom between the old and new cut-off. In recent years we have learned that, alternatively, one can decouple these degrees of freedom by means of local unitary transformations (disentanglers). The result is a reversible renormalization group flow, and an efficient description of many-body ground states. In this talk, I will show you pretty drawings and will use fancy names, such as "multi-scale entanglement renormalization ansatz" (MERA). MERA is currently studied as a possible lattice realization of the AdS/CFT correspondence. I will keep it simple.

We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. Assuming that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, we calculate the spectrum of scalar and tensor perturbations after the bounce, assuming initial quantum vacuum fluctuations. We find that the modes that exit the (sound) Hubble radius during matter-domination when the effective equation of state is slightly negative due to the cosmological constant will be nearly scale-invariant with a slight red tilt, in agreement with observations. The tensor perturbations are also nearly scale-invariant, and the predicted tensor-to-scalar ratio is small.  Finally, as this scenario predicts a positive running of the scalar index, it can be differentiated from inflationary models.

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.