Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras

TL;DR

This paper introduces a new super-Jordanian twist for the $osp(1|4)$ superalgebra, leading to novel deformations of D=4 $AdS$ and Poincare superalgebras with explicit Hopf superalgebra structures.

Contribution

It develops a super-Jordanian twist for $osp(1|4)$ and derives a $ ext{Kappa}$-deformation of the D=4 Poincare superalgebra through contraction.

Findings

Explicit super-Jordanian twist formulas for $osp(1|4)$

New $ ext{Kappa}$-deformation of D=4 Poincare superalgebra

Light cone $ ext{Kappa}$-deformation of Poincare symmetries

Abstract

We consider a superextension of the extended Jordanian twist, describing nonstandard quantization of anti-de-Sitter ($AdS$) superalgebra $osp(1|4)$ in the form of Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of $osp(1|4)$ are given in explicit form. The nonlinear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is to interpret the new super-Jordanian deformation of $osp(1|4)$ superalgebra as deformed D=4 $AdS$ supersymmetries. Subsequently we perform suitable contraction of quantum Jordanian $AdS$ superalgebra and obtain new $\kappa$-deformation of D=4 Poincare superalgebra, with the bosonic sector describing the light cone $\kappa$-deformation of Poincare symmetries.