The algebraic structure of Galilean superconformal symmetries

Details The algebraic structure of Galilean superconformal symmetries The algebraic structure of Galilean superconformal symmetries

2011-05-17

arxiv.org/abs/1105.3444v4

Phys.Rev.D84:065002,2011

Physics

Mathematical Physics

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

Scientific paper

10.1103/PhysRevD.84.065002

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;\alpha) if \alpha=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.

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