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

Abstract

Abstract We present, for the first time, the complete off-shell 4D, N $$ \mathcal{N} $$ = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the N $$ \mathcal{N} $$ = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields h α s − 1 α ̇ s − 1 + + $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{++} $$ , h α s − 2 α ̇ s − 2 + + $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-2\right)}^{++} $$ and two conjugated complex analytic spinor superfields h α s − 1 α ̇ s − 1 + 3 $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ , h α s − 2 α ̇ s − 1 + 3 $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ , where α(s) := (α 1 . . . α s ), α ̇ $$ \dot{\alpha} $$ (s) := ( α ̇ $$ \dot{\alpha} $$ 1 . . . α ̇ $$ \dot{\alpha} $$ s ). Like in the harmonic superspace formulations of N $$ \mathcal{N} $$ = 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” N $$ \mathcal{N} $$ = 2 Einstein supergravity.

Keywords

• Extended Supersymmetry
• Higher Spin Gravity
• Higher Spin Symmetry
• Superspaces