On conformal, SL(4,R) and Sp(8,R) symmetries of massless fields

The sp(8,R) invariant formulation of free field equations of massless fields of all spins in AdS4 available previously in terms of gauge invariant field strengths is extended to gauge potentials. As a by-product, free field equations for a massless gauge field are shown to possess both su(2,2)∼o(4,2) and sl(4,R)∼o(3,3) symmetry. The proposed formulation is well-defined in the AdS4 background but experiences certain degeneracy in the flat limit that does not allow conformal invariant field equations for spin s>1 gauge fields in Minkowski space. The basis model involves the doubled set of fields of all spins. It is manifestly invariant under U(1) electric-magnetic duality extended to higher spins. Reduction to a single massless field contains the equations that relate its electric and magnetic potentials which are mixed by the conformal transformations for s>1. We use the unfolded formulation approach recalled in the paper with some emphasis on the role of Chevalley-Eilenberg cohomology of a Lie algebra g in g-invariant field equations. This method makes it easy to guess a form of the 4d sp(8,R) invariant massless field equations and then to extend them to the ten-dimensional sp(8,R) invariant space-time. Dynamical content of the field equations is analyzed in terms of σ− cohomology.