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

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.

17 pages, LaTeX, new (re-worked) revised and extended version

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Cited by in corpus (7)

• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Lax pairs for deformed Minkowski spacetimes
• Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Supersymmetric Duality in Deformed Superloop Space
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space