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

Understand

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.