Unconstrained off-shell superfield formulation of 4D, N = 2 supersymmetric higher spins

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