N =4 \u2113-conformal Galilei superalgebras inspired by D(2, 1; \u03b1) supermultiplets

Abstract

N = 4 supersymmetric extensions of the ℓ-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N = 4 superconformal group in one dimension D(2,1;α). If the acceleration generators in the superalgebra form analogues of the irreducible (1, 4, 3)-, (2, 4, 2)-, (3, 4, 1)-, and (4, 4, 0)-supermultiplets of D(2, 1; α), the parameter α turns out to be constrained by Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2, 1; α), α remains arbitrary. An N = 4 ℓ-conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work.