D=4 Extended Galilei Superalgebras with Central Charges

TL;DR

This paper constructs nonrelativistic N-extended Galilei superalgebras with central charges via contraction of Poincare superalgebras, revealing new algebraic structures and relations to conformal superalgebras.

Contribution

It introduces a method to derive extended Galilei superalgebras with central charges from Poincare superalgebras, expanding the understanding of nonrelativistic supersymmetry.

Findings

Derived N-extended Galilei superalgebras with central charges.

Showed the algebraic structure depends on the choice of central charge dependence on light velocity.

Connected the constructed superalgebras to extended Galilei conformal superalgebras.

Abstract

We perform a nonrelativistic contraction of N-extended Poincare superalgebra with internal symmetry U(N) and general set of N(N-1) real central charges. We show that for even N=2k and particular choice of the dependence of Z_{ij} on light velocity c one gets the N-extended Galilei superalgebra with unchanged number of central charges and compact internal symmetry algebra U(k;H)=USp(2k). The Hamiltonian positivity condition is modified only by one central charge. If we put all the central charges equal to zero one gets the 2k-extended Galilei superalgebra as the subalgebra of recently introduced extended Galilei conformal superalgebra [1,2].