Exact Results in Noncommutative ${\cal N}=2$ Supersymmetric Gauge Theories

TL;DR

This paper derives exact low-energy effective actions for noncommutative N=2 supersymmetric U(N) gauge theories, revealing decoupling of U(1) and the applicability of Seiberg-Witten solutions for SU(N) in the infrared.

Contribution

It provides the first exact results for the derivative expansion of the Wilsonian effective action in noncommutative N=2 gauge theories, including instanton calculations.

Findings

U(1) sector exhibits IR/UV mixing

SU(N) sector follows commutative Seiberg-Witten solution

U(1) decouples in the infrared regime

Abstract

We study the low-energy dynamics of noncommutative $\N=2$ supersymmetric U(N) Yang-Mills theories in the Coulomb phase. Exact results are derived for the leading terms in the derivative expansion of the Wilsonian effective action. We find that in the infrared regime the U(1) subgroup decouples, and the remaining SU(N) is described by the ordinary commutative Seiberg-Witten solution. IR/UV mixing is present in the U(1), but not in SU(N). Our analysis is based on explicit perturbative and multi-instanton calculations.