Spinor description of the curvatures of D=5 gauge fields

Spinor description of the curvatures of D = 5 Yang-Mills, Rarita-Schwinger, and gravitational fields is considered. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are studied. 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 parameterizing coset manifold SO(1, 4)/(SO(1, 1)×ISO(3)) isomorphic to the three-sphere is considered.