Ring Structure of SUSY * Product and 1/2 SUSY Wess-Zumino Model

TL;DR

This paper investigates the ring structure formed by 1/2 supersymmetric F-terms under the supersymmetric star product in deformed supersymmetric theories, demonstrating the preservation of partial supersymmetry in the Wess-Zumino model.

Contribution

It introduces a novel ring structure based on the supersymmetric star product, clarifying how 1/2 SUSY invariance is maintained in deformed models.

Findings

Identifies a ring structure corresponding to 1/2 SUSY F-terms.

Shows the 1/2 SUSY invariance of the Wess-Zumino model.

Clarifies the impact of supersymmetric star product on supersymmetry preservation.

Abstract

There are two types of non(anti-)commutative deformation of D=4, N=1 supersymmetric field theories and D=2, N=2 theories. One is based on the non-supersymmetric star product and the other is based on the supersymmetric star product . These deformations cause partial breaking of supersymmetry in general. In case of supersymmetric star product, the chirality is broken by the effect of the supersymmetric star product, then it is not clear that lagrangian or observables including F-terms preserve part of supersymmetry. In this article, we investigate the ring structure whose product is defined by the supersymmetric star product. We find the ring whose elements correspond to 1/2 SUSY F-terms. Using this, the 1/2 SUSY invariance of the Wess-Zumino model is shown easily and directly.