Quantum Gravity

I will talk about the relation between non-local theories and gravity. The main thesis is that non-local field theories naturally induce gravity, even at the classical level. Supporting this idea, I will study bi-local scalar field theories, which involve minimal deviations from locality. We will treat them both, bi-local theories and gravity perturbatively. We will see that bi-local theories encode gravity together with higher spin fields.

I will discuss the role(s) of the Immirzi parameter in Loop Quantum Gravity, insisting on the Poisson algebra formed by Thiemann's complexifier, the volume and the Hamiltonian constraint. In particular, we will see how loop quantum cosmology is a direct quantization of this CVH Poisson algebra and how cosmological evolution amounts to a flow in the Immirzi parameter.

In this talk, I will discuss the asymptotic safety paradigm, and will highlight that it can provide a framework for a predictive ultraviolet completion for gravity and matter. Specifically, I will discuss compelling hints that exist for the realization of asymptotic safety in pure gravity, and will then present recent progress on the case of gravity coupled to Standard Model matter. In particular, I will highlight results that show how to forge a link between physics at the Planck scale and physics at the electroweak scale, in order to impose observational constraints on the microscopic quantum gravity dynamics.

I will explain how cosmological dynamics emerge from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

By applying loop quantum gravity techniques to 2+1 gravity with a positive cosmological constant Λ, we show how the local gauge symmetry of the theory encoded in the constraint algebra acquires the quantum group structure of SOq(4). By means of an Inonu-Wigner contraction of the quantum group bi-algebra we obtain the kappa-Poincaré algebra of the flat quantum space-time symmetries.

In this talk we present the study of canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to a new type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge c = 3. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary SU(2) gauge symmetry is recovered via the action of the U(1) 3 Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation.

(Based on the joint work with Laurent Freidel and Alejandro Perez arXiv:1611.03668)

It is a common expectation in quantum gravity that the fundamental nature of space-time would be radically different from the smooth continuum of classical general relativity. In this talk it shall be shown that a quantum modification from loop quantum gravity crucial for singularity resolution is also responsible for deforming the underlying space-time in a manner which cannot be realized using classical geometric structures. With the minimum requirement that the quantum theory satisfies a well-defined notion of covariance explicit midisuperspace models manifesting such non-Riemannian space-times shall be shown to exhibit the physical phenomenon of non-singular signature change. Robustness and implications of this effect shall also be briefly discussed.

I describe how, within the group field theory (GFT) formalism for quantum gravity, we can: 

1) provide a candidate description of the quantum building blocks of spacetime, bringing together ideas and mathematical structures from other quantum gravity formalisms;

2) apply powerful tools from quantum field theory, like the (perturbative and non-perturbative) renormalization group, to establish the quantum consistency of given GFT models and to study their continuum limit and phase structure;

3) extract, from the full theory, an effective cosmological dynamics for the universe described as a quantum condensate of GFT building blocks; in the simplest approximation, this dynamics reduces to the Friedmann equations at large scales but replaces the classical big bang singularity with a quantum bounce.

In this talk, I will address a major conceptual and technical concern of non-perturbative quantum gravity: the quantum superposition of causal structures of space-times. I will discuss a class of theories that can address the problem, their flaws, and their relation to general relativity.

Einstein's causality is one of the fundamental principles underlying modern physical theories. Whereas it is readily implemented in classical physics founded on Lorentzian geometry, its status in quantum theory has long been controversial. It is usually believed that the quantum nature of spacetime at small scales induces the breakdown of causality, although there is no empirical evidence that would support such a view. In my talk, I will argue that one can have a sound notion of causality even in a `quantum spacetime' -- understood as the space of states of an abstract algebra of observables. To this end I will draw from the mathematical richness of noncommutative geometry a la Connes. I will illustrate the general concept with an `almost commutative' toy-model and discuss the potential emprical consequences.