N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras

TL;DR

This paper introduces new supertwist deformations of N=1 Poincare and Euclidean superalgebras, leading to novel quantum superspaces with Lie-algebraic noncommutativity, offering an alternative to existing SUSY deformation schemes.

Contribution

It presents a large class of supersymmetric classical r-matrices and detailed new supertwists for N=1 Poincare and Euclidean superalgebras, enhancing the understanding of quantum superspaces.

Findings

New supertwist deformations of superalgebras

Quantum superspaces with Lie-algebraic noncommutativity

Alternative to Seiberg's star product deformation scheme

Abstract

We present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincare and Euclidean superalgebras. We consider in detail new family of four supertwists of N=1 Poincare superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D=4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the N=1/2 SUSY Seiberg's star product deformation scheme.