We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories maintain their causal properties, but do not have a preferred proper-time foliation. An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity.
Spacetime covariance in canonical quantum gravity is tied to the existence of an anomaly free representation of its constraint algebra. I will argue that establishing the existence of such a representation in the LQG context requires the consideration of higher than unit density weight Hamiltonian constraints.
The struggle between local and global concepts in physics comes to a head in causal set quantum gravity. Local physics -- and general relativity in particular -- must be recovered in a continuum approximation if the theory is to be successful but causal sets are inherently non-local entities.
Spin foam models are models for space time built from discrete chunks of quantized geometry. In the asymptotic regime the classical geometry is regained.
In the last year we have seen rapid developments in our understanding of this geometry at the level of the entire partition function. In particular it was found that the geometries that contribute to the partition function in the asymptotic regime satisfy accidental curvature constraints.
Recently there are a lot of progresses in developing the spinfoam formulation of loop quantum gravity. In this talk I give an overview of the subject. I introduce the formalism and the motivation of the theory, and I discuss the application of spinfoam formulation in black hole and cosmology. I also discuss the inclusion of the quantum matter fields and cosmological constant in the formalism. The inclusion of cosmological constant motivates a Chern-Simons formulation of LQG.
I will present the recently obtained non perturbative 1/N expansion of tensor models. The correlation functions are shown to be analytic in the coupling constant in some domain of the complex plane and to support appropriate scaling bounds at large N. Surprisingly, the non perturbative setting turns out to be a powerful computational tool allowing the explicit evaluation order by order (with bounded rest terms) of the correlations.
The perturbative S-matrix of General Relativity has a rich and fascinating geometric structure that is completely obscured by its traditional description in terms of Feynman diagrams. I'll explain a new way of looking at four dimensional supergravity: as a string theory in twistor space. All tree-level amplitudes in the theory can be described by algebraic curves in Penrose's nonlinear graviton
I will review the reformulation of the loop gravity phase space in terms of spinor networks and twistor networks, and present how these techniques can be used to write spinfoam amplitudes as discretized path integrals and to study the dynamics that they define (recursion, Hamiltonian constraints as differential equations).