Talks

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.

A modified gravity (MOG) theory is explored that can explain current observational data in the present universe without detectable dark matter. This data includes galaxy rotation curves, cluster dynamics, gravitational lensing, globular clusters, the Bullet Cluster and solar system experiments. A vector field in the MOG action is a hidden, dark and massive photon that acts as a collisionless particle in the early universe and explains structure growth. The vector field evolves to an ultralight hidden photon in the present universe after the formation of stars and galaxies, and it cannot play the role of detectable dark matter. The theory successfully describes the CMB data. The matter power spectrum is fitted without dark matter and can distinguish between modified gravity and dark matter scenarios in the present universe.

Gravity in 1+1 dimension is classically trivial but, as shown by A. Polyakov in 1981, it is a non-trivial quantum theory, in fact a conformal field theory (the Liouville theory), and also a string theory. In the last decades many important results and connexions with various areas of mathematics and theoretical physics have been established, but some important issues remain to be understood. In this colloquium I shall focus on some recent developments and new questions on the relation between discrete and continuous 2 dimensional gravity, probabilities and stochastic processes, random fractal geometries and SLE curves.

I will describe how to define a proper RG flow in the space of
tensor networks, with applications to the evaluation of classical
partition functions, euclidean path integrals, and overlaps of tensor
network states.