N=1/2 Global SUSY: R-Matrix Approach

TL;DR

This paper develops a method using R-matrices to construct supersymmetric extensions of Euclidean groups that preserve N=1/2 supersymmetry, leading to quantum supergroups acting on deformed superspaces with non(anti)commuting parameters.

Contribution

It introduces a novel R-matrix approach to build supersymmetric quantum groups with N=1/2 supersymmetry, extending the Euclidean group to deformed superspaces.

Findings

Constructed supersymmetric quantum supergroups using R-matrix method.

Defined non(anti)commuting parameters satisfying specific relations.

Showed global symmetry transformations act on deformed superspaces similarly to classical cases.

Abstract

R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts of appropriately twisted Euclidean superalgebras. The corresponding generalized global symmetry transformations act on deformed superspaces as the usual ones do on undeformed spaces. However, they depend on non(anti)commuting parameters satisfying (anti)commutation relations defined by relevant R matrix.