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.

I will present a new approach to information-theoretic foundations of quantum theory, that does not rely on probability theory, spectral theory, or Hilbert spaces. The direct nonlinear generalisations of quantum kinematics and dynamics are constructed using quantum information geometric structures over algebraic states of W*-algebras (quantum relative entropies and Poisson structure). In particular, unitary evolutions are generalised to nonlinear hamiltonian flows, while Lueders? rules are generalised to constrained relative entropy maximisations. Orthodox probability theory and quantum mechanics are special cases of this framework. I will also discuss the epistemic interpretation associated with this approach (rendering quantum theory as a framework for ontically noncommittal causal inference), as well as the possibility of deriving emergent space-times directly from quantum models.

A featureless insulator is a gapped phase of matter that does not exhibit fractionalization or other exotic physics, and thus has a unique ground state. The classic albeit non-interacting example is an electronic band insulator. A standard textbook argument tells us that band insulators require an even number of electrons -- an integer number for each spin -- per unit cell. I will explore the converse question: given such an 'integer filling', is a featureless insulating state possible?  I will demonstrate that in most three-dimensional crystals, an insulating ground state cannot be unique -- and hence cannot be featureless -- except at certain special fillings fixed by the crystalline space group. This result, which remains valid more generally for interacting systems of fermions, bosons, or spins (as long as they have a conserved U(1) charge), relies on a combination of topological 'flux insertion' arguments and elementary crystallographic ideas. I will explore its implications through examples ranging from band theory, where it leads to the identification of protected semimetals, to frustrated magnetism, where it suggests new venues for spin liquid physics.

References: S.A. Parameswaran, A.M. Turner, D.P. Arovas and A. Vishwanath, Nature Physics 9, 299 (2013).
(see also related work in PNAS 110, 16378 (2013) and Phys. Rev. Lett. 110, 125301 (2013).)