Abstract
The spectrum of IIB supergravity on AdS${}_5 \times S^5$ contains a number of bound states described by long double-trace multiplets in $\mathcal{N}=4$ 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 $\tfrac{1}{N^2}$ 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.
Highlights
Much progress has been made in understanding the structure of the spectrum of double-trace operators in N 1⁄4 4 super Yang-Mills theory at large N and large ‘t Hooft coupling λ 1⁄4 g2N [1]
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
Summary
Much progress has been made in understanding the structure of the spectrum of double-trace operators in N 1⁄4 4 super Yang-Mills theory at large N and large ‘t Hooft coupling λ 1⁄4 g2N [1] Based on these results, operator product expansion (OPE) and bootstrap techniques have been applied in [2,3] to obtain closed form expressions for supergravity loop corrections of certain holographic correlators, uncovering novel and rich structure (see [4,5] for related approaches to such loop corrections). We complete the picture for the double-trace spectrum and conjecture a general formula for the leading anomalous dimensions of all long double-trace operators of any twist, spin, and suð4Þ representation. III) leads us to the following conjecture, generalizing results in [1,2,3]
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