Constructive Renormalization of the 2-dimensional Grosse-Wulkenhaar Model with Multiscale Loop Vertex Expansions

Abstract: In this paper we construct the noncommutative Grosse-Wulkenhaar model on 2-dimensional Moyal plane with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.