Higher spin holography for SYM in d dimensions

We derive the spectrum of gauge invariant operators for maximally supersymmetric Yang–Mills theories in d dimensions. After subtracting the tower of BPS multiplets, states are shown to fall into long multiplets of a hidden SO ( 10 , 2 ) symmetry dressed by thirty-two supercharges. Their primaries organize into a universal, i.e., d -independent pattern. The results are in perfect agreement with those following from (naive) KK reduction of type II strings on the warped AdS × S near-horizon geometry of D p -branes