Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model

TL;DR

This paper presents a non-perturbative construction of the 2D Grosse-Wulkenhaar model using loop vertex expansion, demonstrating renormalization and Borel summability in a non-commutative quantum field theory.

Contribution

It introduces a novel non-perturbative approach to construct and renormalize a non-commutative quantum field theory model for the first time.

Findings

Successful renormalization of the 2D Grosse-Wulkenhaar model

Proof of Borel summability of the perturbation series

First non-perturbative construction of a non-commutative QFT model

Abstract

In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model 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.