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;\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