New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models

A novel feature of the Z2×Z2-graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the “exotic bosonic coordinate” was not considered by previous works on the one-dimensional Z2×Z2-graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained. The graded superspace calculus of the Z2×Z2-graded worldline super-Poincaré algebra induces two-dimensional Z2×Z2-graded relativistic models; they are invariant under a new Z2×Z2-graded 2D super-Poincaré algebra which differs from the previous two Z2×Z2-graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S1, a Z2×Z2-graded closed string with periodic boundary conditions is derived. The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger (β-deformed, where β≥0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β=0) is obtained. While the spectrum of the β=0 point-particle models is degenerate (due to its relation with an N=2 supersymmetry), this is no longer the case for the β>0 models.