Quantum Gravity

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.

Constraint free initial data can be given for vacuum general relativity on a pair of intersecting null hypersurfaces. Moreover, the Poisson algebra of a set of such free null initial data has been found,but it has an unfamiliar structure, making its quantization difficult. We note that this algebra is essentially a sum of an infinite number of copies of the Poisson algebras of cylindrically symmetric gravity. Using the fact that cylindrically symmetric gravity is integrable we find new free data with an algebra more amenable to quantization.

Abstract:  Complex networks describe interacting systems ranging from the brain to the Internet. While so far the geometrical nature of complex networks has been mostly neglected, the novel field of network geometry is crucial for gaining a deeper theoretical understanding of the architecture of complexity. At the same time, network geometry is at the heart of quantum gravity, since many approaches to quantum gravity assume that space-time is discrete and network-like at the quantum level. In network geometry a crucial problem is the identifications of mechanisms to describe emergent network geometry. In this talk, after an introduction to complex network theory, l will present a class of non–equilibrium models [1-4] in which geometrical properties of the networks emerge spontaneously from their dynamics. Specifically we will discuss the model called network geometry with flavor (NGF).The NGF can generate discrete geometries of different nature, ranging from chains and higher dimensional manifolds to scale-free complex networks. Interestingly the NGF with fitness of the nodes reveals relevant relations with quantum statistics. In fact the faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann or Bose-Einstein statistics depending on their flavor and on their dimensionality. Specifically, NGFs with flavor s=-1, when constructed in dimension d=3 gluing tetrahedra along their triangular faces, have the generalized degrees of the triangular faces, of the links, and of the nodes following respectively the Fermi-Dirac, the Boltzmann or the Bose-Einstein distribution. 

[1] G. Bianconi, Interdisciplinary and physics challenges in network theory, EPL 111, 56001 (2015).
[2] Z. Wu, G. Menichetti C. Rahmede G. Bianconi, Emergent Complex Network Geometry, Scientific Reports 5, 10073 (2015).
[3] G. Bianconi and C. Rahmede, Complex Quantum Network Manifolds are Scale-Free in d>2, Scientific Reports 5, 13979 (2015)
[4] G. Bianconi and C. Rahmede, Network geometry with flavor: from complexity to quantum geometry, arxiv:1511.04539 (2015)

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.