Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems

TL;DR

This paper explores a deformed superspace where coordinates follow a Clifford algebra, revealing new (non)renormalization theorems and properties of N=1/2 supersymmetric theories, including vacuum stability and radiative corrections.

Contribution

It introduces and proves novel (non)renormalization theorems in deformed superspace, showing how F-terms and Fbar-terms behave differently under quantum corrections.

Findings

F-term becomes radiatively corrected and resembles a D-term

Fbar-term remains unrenormalized

Vacuum energy remains zero to all orders

Abstract

We consider a deformed superspace in which the coordinates \theta do not anticommute, but satisfy a Clifford algebra. We present results on the properties of N=1/2 supersymmetric theories of chiral superfields in deformed superspace, taking the Wess-Zumino model as the prototype. We prove new (non)renormalization theorems: the F-term is radiatively corrected and becomes indistinguishable from the D-term, while the Fbar-term is not renormalized. Supersymmetric vacua are critical points of the antiholomorphic superpotential. The vacuum energy is zero to all orders in perturbation theory. We illustrate these results with several examples.