Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces

TL;DR

This paper explores a quantum group approach to non-anticommutative deformations in Euclidean supersymmetric theories, constructing twist deformations and demonstrating covariance of superfield actions under these deformations.

Contribution

It introduces a novel twist deformation framework for superspaces and Lie superalgebras, ensuring manifest invariance of superfield actions in non-anticommutative settings.

Findings

Constructed twist deformations using left supersymmetry generators

Demonstrated covariance of superfield $ ext{star}$-products

Ensured invariance of superfield actions under deformed symmetries

Abstract

We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and Lie superalgebras are constructed in terms of the left supersymmetry generators. Non-anticommutative $\star$-products of superfields are covariant objects in the twist-deformed supersymmetries, and this covariance guarantees the manifest invariance of superfield actions using $\star$-products.