Renormalization of noncommutative Yang-Mills theories: A simple example

TL;DR

This paper demonstrates through explicit calculations that certain noncommutative Yang-Mills theories are renormalizable, supporting the conjecture that these models can be consistently defined at quantum level.

Contribution

It provides a concrete example of renormalization in noncommutative Yang-Mills theories using explicit Feynman graph calculations.

Findings

Feynman graphs with repeated insertions are renormalizable by local counterterms.

Supports the renormalizability conjecture of noncommutative Yang-Mills models.

Explicit calculations confirm the theoretical expectations.

Abstract

We prove by explicit calculation that Feynman graphs in noncommutative Yang-Mills theory made of repeated insertions into itself of arbitrarily many one-loop ghost propagator corrections are renormalizable by local counterterms. This provides a strong support for the renormalizability conjecture of that model.