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

TL;DR

This paper develops a non-perturbative construction of the 2D Grosse-Wulkenhaar noncommutative quantum field theory using multiscale loop vertex expansions, demonstrating Borel summability and renormalization.

Contribution

It introduces a novel non-perturbative approach to construct and renormalize a noncommutative quantum field theory model.

Findings

First non-perturbative construction of the 2D Grosse-Wulkenhaar model

Proves Borel summability of the perturbation series

Successfully applies loop vertex expansion to noncommutative QFT

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.