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Register a new userN=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
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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 Seibergs star product deformation scheme.
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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.
We show how some classical r-matrices for the D=4 Poincare algebra can be supersymmetrized by an addition of part depending on odd supercharges. These r-matrices for D=4 super-Poincare algebra can be presented as a sum of the so-called subordinated r-matrices of super-Abelian and super-Jordanian type. Corresponding twists describing quantum deformations are obtained in an explicit form. These twists are the super-extensions of twists obtained in the paper arXiv:0712.3962.
We present the class of deformations of simple Euclidean superalgebra, which describe the supersymmetrization of some Lie algebraic noncommutativity of D=4 Euclidean space-time. The presented deformations are generated by the supertwists. We provide new explicit formulae for a chosen twisted D=4 Euclidean Hopf superalgebra and describe the corresponding quantum covariant deformation of chiral Euclidean superspace.
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of superconformal groups SU(2,2|N) and OSp(8*|2n) in four and six dimensions were constructed as minreps and their U(1) and SU(2) deformations, respectively. In this paper we extend these results to SU(2) deformations of the minrep of N=4 superconformal algebra D(2,1;lambda) in one dimension. We find that SU(2) deformations can be achieved using n pairs of bosons and m pairs of fermions simultaneously. The generators of deformed minimal representations of D(2,1;lambda) commute with the generators of a dual superalgebra OSp(2n*|2m) realized in terms of these bosons and fermions. We show that there exists a precise mapping between symmetry generators of N=4 superconformal models in harmonic superspace studied recently and minimal unitary supermultiplets of D(2,1;lambda) deformed by a pair of bosons. This can be understood as a particular case of a general mapping between the spectra of quantum mechanical quaternionic Kahler sigma models with eight super symmetries and minreps of their isometry groups that descends from the precise mapping established between the 4d, N=2 sigma models coupled to supergravity and minreps of their isometry groups.
We provide the classification of real forms of complex D=4 Euclidean algebra $mathcal{epsilon}(4; mathbb{C}) = mathfrak{o}(4;mathbb{C})) ltimes mathbf{T}_{mathbb{C}}^4$ as well as (pseudo)real forms of complex D=4 Euclidean superalgebras $mathcal{epsilon}(4|N; mathbb{C})$ for N=1,2. Further we present our results: N=1 and N=2 supersymmetric D=4 Poincare and Euclidean r-matrices obtained by using D= 4 Poincare r-matrices provided by Zakrzewski [1]. For N=2 we shall consider the general superalgebras with two central charges.
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