Mathematical Physics Seminars 2016 - 2017

  Monday 16 January 2017, 14:00, room 114

Pietro Dona (CPT, Marseille) : Cosmological applicatiaons of coherent states

In this talk we will consider two applications of group coherent states to cosmology. Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince you that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of quantum fields. Furthermore we approach the problem of finding generalized states for matter fields in a de Sitter universe, moving from a group theoretical point of view. This has profound consequences for cosmological perturbations during inflation, and for other CMB observables.

  Monday 9 January 2017, 14:00, room 114

Marc Geiller (Perimeter Institute, Canada) : Quantum gravity and topological quantum field theories with defects

In this talk, I will present and explain the structure of vacua underlying the quantum representation and the Hilbert space of loop quantum gravity and related discrete non-perturbative approaches to quantum gravity. This will highlight an unsuspected richness of this class of theories, and make transparent their interpretation as topological quantum field theories with defects. These are theories which posses no local degrees of freedom in the bulk, but can however carry quasi-particle-like excitations on defects of arbitrary co-dimension. Interestingly, such theories have recently attracted lots of attention in condensed matter, where it is believed that they provide a classification of the so-called topologically-ordered phases of matter. On the quantum gravity side, I will explain the relevance of this construction for the study of the continuum limit and of entanglement entropy in gravity and lattice gauge theories.

  Monday 9 January 2017, 11:00, room 114

Sylvain Carrozza (Perimeter Institute, Canada) : Quantum fields with tensorial locality

In recent years, generalizations of matrix models known as Tensor Models and Group Field Theories have been developed into a consistent formalism. The common feature of these field theories is an abstract notion of locality, know as tensorial locality, which encodes the combinatorial structure of the elementary field interactions. It has initially been introduced in the context of quantum gravity, where indeed the absence of a non-dynamical background space-time renders the standard notion of locality inoperative. I will provide an overview of this approach, focusing on general features of the phase diagrams of tensorial theories, and of their possible applications to quantum gravity and statistical physics. I will in particular discuss the tensorial version of the Sachdev-Ye-Kitaev model recently proposed by Witten.

  Wednesday 4 January 2017, 14:00, room 114

Pierre Martinetti (Dipartimento di Matematica, Università di Genova (Italy)) : Tordre une transformation de jauge en géométrie non-commutative.

Récemment ont été proposés en géométrie non-commutative des modèles « au delà du modèle standard », qui utilisent des triplets spectraux tordus (« twisted »). On verra comment implémenter une transformation de jauge dans ce contexte, et en particulier comment tordre la transformation de jauge pourrait s’interpréter comme un changement de signature de la métrique.

  Monday 12 December 2016, 14:00, room 114

Daniele Pranzetti (SISSA, Trieste, Italy) : Generalized GFT condensates and horizon entropy

I present the construction, in the group field theory formalism, of a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. I apply the construction to the case of a continuum spherically symmetric quantum geometry of an horizon and I show how the associated reduced density matrix manifestly exhibits an holographic behavior.

  Monday 5 December 2016, 15:00, room 110 (cosmo room)

Dine Ousmane Samary (Albert Einstein Institute, Golm, Germany) : Functional renormalization group analysis for a U(1) TGFT

This talk is focused on the functional renormalization group applied to the tensor model on the Abelian group U(1) with closure constraint. We show how Ward-Takahashi identities and Schwinger-Dyson equations can help to provide a suitable truncation around the marginal interactions with respect to the perturbative power counting. The behaviour around the Gaussian fixed point is given. We find the existence of several non-trivial fixed points and study the physical outcome around these.

  Thursday 24 November 2016, 14:00, room 114

Philippe Mathieu (LAPTH, Annecy-le-Vieux, France) : Relations between abelian Chern-Simons and BF topological quantum field theories and Reshetikhin-Turaev and Turaev-Viro topological invariants.

Deligne-Beilinson (DB) cohomology classifies U(1)-connexions on 3-manifolds. The structure of DB classes provides thus a way to perform exact computations in abelian Chern-Simons (CS) theory (resp. BF Theory) at the level of functional integrals. Partition functions and expectation values appear then to be strongly related to Reshetikhin-Turaev (RT) (resp. Turaev-Viro (TV)) topological invariant of 3-manifolds.

In the non-abelian case, it is has been known for a few decades that :

1-The modulus square of CS partition function is equal to the BF partition function 2-The modulus square of RT topological invariant is equal to the TV topological invariant 3-The CS partition function is equal to the RT topological invariant

We will see that, thanks to DB cohomology, those relations are not true in the abelian case, showing that this abelian case is not a trivial subcase of the non-abelian one.

  Monday 7 November 2016, 14:00, room 114

Yuki Sato (Chulalongkorn University, Bangkok, Thailand) : ’’Quantum criticality’’ from Ising model on dynamical triangulations

We argue the classical Ising model coupled to 2d dynamical triangulations based on the Hermitian two matrix model and show that even though the Ising model is classical, the Curie temperature can reach the absolute zero by tuning a parameter controlling simplicial geometries. This talk is based on a work in progress with Tomo Tanaka in Rikkyo University, Japan.