Renormalizable Tensor Field Theories

Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.Comment: Based on the talk Tensor Models and Renormalization given at the International Congress on Mathematical Physics, ICMP2015, 27th July - 1st August, 2015, Santiago de Chile, Chil

Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field

We prove that the beta function of the Grosse-Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared fixed point. Some consequences of these results are discussed.Comment: 14 pages, 5 figure