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