Abstract
Using the off-shell formulation for mathcal{N} = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main mathcal{N} = 2 results are then generalised to the mathcal{N} -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin mathcal{N} = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the mathcal{N} = 2 superconformal group.
Highlights
Using the off-shell formulation for N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials
One of the goals of this paper is to extend some of the results of [3,4,5,6] to the 4D N = 2 superconformal case
In this work we make use of N = 2 conformal superspace [19], which is an ultimate formulation for N = 2 conformal supergravity in the sense that any different off-shell formulation is either equivalent to it or is obtained from it by partially fixing the gauge freedom
Summary
We restrict our attention to conformally flat superspaces In these geometries it may be shown that the chiral descendants (3.7) are gauge-invariant δζ,λWα(m+n+2)(Υ) = 0 , δζ,λWα(m+n+2)(Υ ) = 0. Just as for the n = 0 case, the action (3.21) proves to be gauge-invariant and the field strengths (3.18) are linearised higher-spin super-Weyl tensors. The conformal higher-spin N = 2 supercurrents and their dual gauge prepotential were introduced in the previous sections for an arbitrary conformal supergravity background. A primary tensor superfield Jα(m)α (n) defined on the background superspace will be called a conformal supercurrent if it obeys. Requiring both the prepotentials Υα(m)α (n), m, n ≥ 0, and corresponding gauge parameters to be primary uniquely fixes the dimension and U(1)R charge of the former: 4(N
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