Double-trace spectrum of N=4 supersymmetric Yang-Mills theory at strong coupling.

The spectrum of IIB supergravity on AdS5 × S5 contains a number of bound states described by long double-trace multiplets in N ¼ 4 super Yang-Mills theory at large ‘t Hooft coupling. At large N these states are degenerate and to obtain their anomalous dimensions as expansions in 1 N2 one has to solve a mixing problem. We conjecture a formula for the leading anomalous dimensions of all long double-trace operators which exhibits a large residual degeneracy whose structure we describe. Our formula can be related to conformal Casimir operators which arise in the structure of leading discontinuities of supergravity loop corrections to four-point correlators of half-BPS operators