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| Paper IPM / P / 16846 | ||||||||||||||||||
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We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in four-dimensional Minkowski space-time, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description \cite{Najafizadeh:2019mun}, we employ an auxiliary field to close the algebra of supersymmetry transformations off-shell. The 4D N=1 massless continuous spin supermultiplet is then denoted by (Φ,H;Ψ), comprised of a dynamical and a non-dynamical complex scalar continuous spin gauge fields Φ and H, as well as a Dirac continuous spin gauge field Ψ. In particular, we demonstrate that the continuous spin supermultiplet, in a limit, reproduces off-shell supersymmetry transformations of the scalar (chiral) supermultiplet (0,1/2), all integer-spin supermultiplets (s,s+1/2),s⩾, and all half-integer spin supermultiplets (\, s\, {\scriptstyle -\, 1/2}\,,\, s \,\,),\, s\geqslant1.
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