Quantum Gravity

Although the inflationary predictions for the primordial power spectrum of    density inhomogeneities   seem  very successful, there is an obscure part in our understanding of the emergence of the seeds of cosmic   structure:  How  does  a universe which at one pint  in time is described by a  state that is fully  homogeneous and isotropic,  evolve into a state that is not,   given that the dynamics  does not  contain any  source  for the  undoing of  such symmetry?   We will  discuss  an   approach that  offers  a resolution  of the  issue  in the context of  proposals to deal  with the measurement  problem in quantum  mechanics. We will  see that the   approach  naturally  resolves the difficulties  raised  by the  lack of  observation of tensor modes.

Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.

In order to introduce the cosmological constant in a simplicial geometry, constant curvature should be introduced on simplex faces. This yields a compactification of the phase space and the finiteness of the Hilbert for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space.

Quantum effects render black holes unstable.  Besides Hawking radiation there is another, genuinely quantum gravitational, source of instability: the Hajicek-Kiefer explosion via tunnelling to a white hole.  A recent result in classical general relativity makes this decay channel plausible: there is an exact external solution of the Einstein equations locally (but not globally) isometric to extended Schwarzschild, which describes an object collapsing into a black hole and then exploding out of a white hole. The tunnelling time can in principle be computed using Loop Quantum Gravity. If it is sufficiently short, present explosions of primordial black hole could be observables, opening a new observational window on quantum gravity. I discuss the possibility that these explosions could be related to the recently observed and mysterious Fast Radio Bursts. 

By explicit construction, I will show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations.

I propose a quantum gravity model in which the fundamental degrees of freedom are pure information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration arising between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension. The model has three quantum phases: a mean field phase in which the spectral and Hausdorff dimensions coincide and are larger then 4. A fluctuations-dominated phase in which the Hausdorff dimension can only be 4 and the spectral dimension is lower than the Hausdorff dimension and a disordered phase in which there is no space-time interpretation. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. An ultraviolet fixed point at the lower critical dimension of the Ising model implies the absence of space-time at very small scales. At finite temperatures the universe emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits also macroscopic black hole configurations corresponding to graphs containing holes with no space time inside and around which there are "Schwarzschild-like horizons" with a lower spectral dimension and an entropy proportional to their surface. 

I will discuss a new duality between strongly coupled and weakly coupled condensed matter systems. It can be obtained by combining the gauge-gravity duality with analog gravity. In my talk I will explain how one arrives at the new duality, what it can be good for, and what questions this finding raises.

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.