Abstract
We present, for the first time, the complete off-shell 4D, mathcal{N} = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the mathcal{N} = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields {h}_{alpha left(s-1right)dot{alpha}left(s-1right)}^{++} , {h}_{alpha left(s-2right)dot{alpha}left(s-2right)}^{++} and two conjugated complex analytic spinor superfields {h}_{alpha left(s-1right)dot{alpha}left(s-1right)}^{+3} , {h}_{alpha left(s-2right)dot{alpha}left(s-1right)}^{+3} , where α(s) := (α1. . . αs), dot{alpha} (s) := ( dot{alpha} 1. . . dot{alpha} s). Like in the harmonic superspace formulations of 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” mathcal{N} = 2 Einstein supergravity.
Highlights
We present, for the first time, the complete off-shell 4D, N = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the N = 2 harmonic superspace approach
Complete off-shell Lagrangian formulation of 4D free higher-spin N = 1 models has been developed in terms of N = 1 superfields in works [11–13] and further applied to study quantum effective action generated by N = 1 superfields in AdS space in [14]
Other aspects of higher-spin supersymmetric field theory are related with supersymmetric extension [41–43] of the Vasiliev theory of interacting higher spin fields
Summary
We will deal with N = 2 harmonic superspace (HSS) in the analytic basis as the following set of coordinates [3–5]. Where we employed the condense notation, μ = (μ, μ ) These transformations leave intact the harmonic analytic subspace of (2.1), ζ :=. With the following analyticity-preserving transformation law under N = 2 supersymmetry, δ x5 = 2i −θ+ − ̄−θ+ This coordinate can be interpreted as associated with the central charge in N = 2 Poincaré superalgebra. In the HSS formalism, one uses a gauge in which the analytic superfield which accommodates this compensating multiplet is gauged away to yield the fundamental group of the resulting Einstein N = 2 SG as the following analyticity-preserving superdiffeomorphisms δλxm = λm(x, θ+, u), δλθ+μ = λ+μ(x, θ+, u), δλθ−μ = λ−μ(x, θ+, θ−, u), δλu±i = 0. With taking into account the residual gauge freedom of the WZ gauge (2.19) (see below), the complete set of essential off-shell degrees of freedom is 40 + 40
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