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The spectrum of IIB supergravity on AdS${}_5 \times S^5$ contains a number ofbound states described by long double-trace multiplets in $\mathcal{N}=4$ superYang-Mills theory at large 't Hooft coupling. At large $N$ these states aredegenerate and to obtain their anomalous dimensions as expansions in$\tfrac{1}{N^2}$ one has to solve a mixing problem. We conjecture a formula forthe leading anomalous dimensions of all long double-trace operators whichexhibits a large residual degeneracy whose structure we describe. Our formulacan be related to conformal Casimir operators which arise in the structure ofleading discontinuities of supergravity loop corrections to four-pointcorrelators of half-BPS operators.

The double-trace spectrum of N=4 SYM at strong coupling