On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields

Understand

The $sp(8, R)$ invariant formulation of free field equations of massless fields of all spins in $AdS_4$ 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 $su(2,2)\sim o(4,2)$ and $sl(4,R)\sim o(3,3)$ symmetry.
• The proposed formulation is well-defined in the $AdS_4$ 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.