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The algebraic structure of Galilean superconformal symmetries

Mathematical Physics 2011-09-29 v4 High Energy Physics - Theory math.MP

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;\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.

Keywords

Cite

@article{arxiv.1105.3444,
  title  = {The algebraic structure of Galilean superconformal symmetries},
  author = {Sergey Fedoruk and Jerzy Lukierski},
  journal= {arXiv preprint arXiv:1105.3444},
  year   = {2011}
}

Comments

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