Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)

TL;DR

This paper computes planar and nonplanar Konishi anomalies in noncommutative N=1 supersymmetric U(1) gauge theory, revealing their roles in deriving the effective superpotential and highlighting nonlocal effects like UV/IR mixing.

Contribution

It introduces the calculation of both planar and nonplanar Konishi anomalies in noncommutative supersymmetric gauge theories and derives the effective superpotential incorporating nonlocal features.

Findings

Planar anomaly is a -deformation of the commutative case.

Nonplanar anomaly exhibits UV/IR mixing and nonlocal Wilson lines.

Effective superpotential depends on gauge-invariant superfields with nontrivial gauge field dependence.

Abstract

The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory arising from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected \star-deformation of the commutative anomaly, nonplanar anomaly reflects the important features of nonplanar diagrams of noncommutative gauge theories, such as UV/IR mixing and the appearance of nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies to calculate the effective superpotential of the theory. In the limit of vanishing |\Theta p|, with \Theta the noncommutativity parameter, the noncommutative effective superpotential depends on a gauge invariant superfield, which includes supersymmetric Wilson lines, and has nontrivial dependence on the gauge field supermultiplet.