The algebraic structure of Galilean superconformal symmetries

Abstract

The semisimple part of d-dimensional Galilean conformal algebra g^(d) is given by h^(d)=O(2,1)+O(d), which after adding via semidirect sum the 3d-dimensional Abelian algebra t^(d) of translations, Galilean boosts and constant accelerations completes the construction. We obtain Galilean superconformal algebra G^(d) by firstly defining the semisimple superalgebra H^(d) which supersymmetrizes h^(d), and further by considering the expansion of H^(d) by tensorial and spinorial graded Abelian charges in order to supersymmetrize the Abelian generators of t^(d). For d=3 the supersymmetrization of h^(3) is linked with specific model of N=4 extended superconformal mechanics, which is described by the superalgebra D(2,1;α) if α=1. We shall present as well the alternative derivations of extended Galilean superconformal algebras for d=1,2,3,4,5 by employing the Inonu-Wigner contraction method.

1 + 18 pages, v4 with corrections in proof added, version in print in PRD

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• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Chiral and Real N=2 supersymmetric l-conformal Galilei algebras
• N = 2 Galilean superconformal algebras with central extension
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of $\mathcal{N}=1$ superconformal Galilei algebras and their representations
• Invariant PDEs with Two-dimensional Exotic Centrally Extended Conformal Galilei Symmetry
• N=4 l-conformal Galilei superalgebra
• Superfield approach to higher derivative N=1 superconformal mechanics
• N=1,2,3 l-conformal Galilei superalgebras
• From $\mathcal{N}=4$ Galilean superparticle to three-dimensional non-relativistic $\mathcal{N}=4$ superfields