Non-renormalizability of noncommutative SU(2) gauge theory

TL;DR

This paper investigates the renormalization properties of noncommutative SU(2) gauge theory, revealing that certain divergences can be renormalized while others cannot, indicating non-renormalizability.

Contribution

It demonstrates the non-renormalizability of noncommutative SU(2) gauge theory at one-loop order in the fermionic sector.

Findings

2-point and 3-point divergences are renormalizable

4-point fermionic divergence is non-renormalizable

Noncommutative SU(2) gauge theory is non-renormalizable at one loop

Abstract

We analyze the divergent part of the one-loop effective action for the noncommutative SU(2) gauge theory coupled to the fermions in the fundamental representation. We show that the divergencies in the 2-point and the 3-point functions in the $\theta$-linear order can be renormalized, while the divergence in the 4-point fermionic function cannot.