Deformations of Euclidean Supersymmetries

TL;DR

This paper studies quantum supergroups from non-anticommutative deformations of Euclidean supersymmetric theories, demonstrating covariance of superfield products and invariance of deformed actions under deformed supersymmetries.

Contribution

It introduces a framework for understanding deformed supersymmetries via twist operators and shows how superfield actions remain invariant under these deformations.

Findings

Non-anticommutative star-products transform covariantly.

Deformed superfield actions are invariant under deformed supersymmetries.

Twist operators contain left spinor generators.

Abstract

We consider quantum supergroups that arise in non-anticommutative deformations of N=(1/2,1/2) and N=(1,1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding deformed algebras of superfields contain left spinor generators. We show that non-anticommutative $\star$-products of superfields transform covariantly in the deformed supersymmetries. This covariance guarantees the invariance of deformed superfield actions of models involving $\star$-products of superfields.