Comments of ${\mathbb{Z}}_2^2$-supersymmetry in superfield formalism

Abstract

We investigate superfield formulation of the minimal ${\mathbb{Z}}_2^2$-supersymmetry. It is shown that the integrability on ${\mathbb{Z}}_2^2$-superspace guarantees the invariance of action. Then we present two superfields which carry distinct irreducible representations of the ${\mathbb{Z}}_2^2$-supersymmetry algebra. One of them gives integrable Lagrangian and the other does not. We also show that integrable superfields with different ${\mathbb{Z}}_2^2$-degree also carry irreducible representations and they give invariant actions. To perform this analysis, the representation theory of the minimal ${\mathbb{Z}}_2^2$-supersymmetry algebra is studied in some detail.

18 pages, no figure

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Cited by in corpus (10)

• Irreducible representations of ${\mathbb{Z}}_2^2$-graded $\mathcal{N}=2$ supersymmetry algebra and ${\mathbb{Z}}_2^2$-graded supermechanics
• New aspects of the Z${}_{\text{2}}$ $\times$ Z${}_{\text{2}}$-graded 1D superspace: induced strings and 2D relativistic models
• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
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• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• On the detectability of paraparticles beyond bosons and fermions