Spinor description of $D=5$ massless low-spin gauge fields

Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with $2s$ indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to $4d$ case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold $SO(1,4)\mathrm{/}(SO(1,1)\times ISO(3))$ isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere $SU(2)\mathrm{/}U(1)$ is proposed. The states in its spectrum are given by the functions on $S^3$ that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various massless supermultiplets of $D=5$ space-time supersymmetry.