Unconstrained off-shell superfield formulation of 4D, $$ \mathcal{N} $$ = 2 supersymmetric higher spins

Abstract

Abstract We present, for the first time, the complete off-shell 4D,$$ \mathcal{N} $$ N = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the $$ \mathcal{N} $$ N = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{++} $$ h α s − 1 α ̇ s − 1 + + , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-2\right)}^{++} $$ h α s − 2 α ̇ s − 2 + + and two conjugated complex analytic spinor superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 1 α ̇ s − 1 + 3 , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 2 α ̇ s − 1 + 3 , where α(s) := (α1. . . αs),$$ \dot{\alpha} $$ α ̇ (s) := ($$ \dot{\alpha} $$ α ̇ 1. . .$$ \dot{\alpha} $$ α ̇ s). Like in the harmonic superspace formulations of $$ \mathcal{N} $$ N = 2 Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content (s,s−1/2,s−1/2,s−1) is restored. For s = 2 the action describes the linearized version of “minimal” $$ \mathcal{N} $$ N = 2 Einstein supergravity.