I am organizing, with Jacques Magnen (École Polytechnique) and Laurent Poinsot (Univ. Paris XIII), on Tuesday the 22nd of November 2011, within the framework of the French "GDR Renormalisation : aspects algébriques, analytiques et géometriques", a one-day meeting at the Henri Poincaré Institute, Hermite amphitheatre.
The programme is the following:
- 10h-11h: Vincent Rivasseau (Laboratoire de Physique Théorique Orsay, France) - "Towards renormalizing Group Field Theory"
- 11h-11h15: coffee break
- 11h15-12h15: Razvan Gurau (Perimeter Institute, Waterloo, Canada) - "Large N limit and critical phenomena in Colored Tensor Models"
Matrix models are one of the most versatile tools in theoretical physics with applications ranging from the theory of strong interaction, to string theory, critical phenomena and two dimensional quantum gravity. In higher dimensions matrix models generalize to tensor models. Ordinary tensor models do not admit a meaningful 1/N expansion, and no analytic result could be establish on their continuum limit. In this talk I will present an overview of the colored tensor models for which many of the fundamental results concerning matrix models can be generalized. I will present their 1/N expansion, discus the leading order graphs (of spherical topology) and the continuum limit of such models.
- 12h-14h: lunch break
- 14h-15h: Aristide Baratin (Institut de Physique Théorique Saclay - Centre de Physique Théorique de l'École Polytechnique - Laboratoire de Physique Théorique Orsay) - "Group field theory: the dynamics of quantum geometry"
- 15h-15h15: coffee break
- 15h15-16h15: Matteo Smerlak (Albert Einstein Institute, Golm, Germany) - "Powercounting in Ponzano-Regge-like models"
I will review recent results, obtained in collaboration with V. Bonzom, concerning the structure of the large-spin divergences of Ponzano-Regge-like models. These involve notions from discrete gauge theory and twisted cohomology, and provide the powercounting estimates needed for Rivasseau's renormalization program to start off.
- 16h15-17h15: Thomas Krajewski (Centre de Physique Théorique Marseille, France) - "Group Field Theory Formulation of Lorentzian Quantum Gravity"
The day will begin with an introductory talk by Vincent Rivasseau. Several recent results will then be presented by the other speakers.
The subject of the workshop is Group Field Theory (GFT), one of today's candidates for a fundamental theory of quantum gravity. These theories have been developed as a generalization of 2-dimensional matrix models to the 3- and 4-dimensional cases. Thus, GFT models are duals to the Ponzano-Regge model, when considering 3-dimensional gravity, or to the Ooguri model, when considering 4-dimensional gravity.
Group field theoretical models can be seen today not only as a technical tool but as a proposal for a quantum formulation of gravitation. Behind this lies the general idea that GFTs are theories OF space-time, while quantum field theories are ON space-time.
The Feynman graphs of these models are tensor graphs, with three strands per edge for three-dimensional models and respectively with four strands per edge for four-dimensional models. These graphs represent a natural generalization of the ribbon graphs of non-commutative quantum field theory.
The rest of the abstracts of the talks will be published here soon.