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

TL;DR

This paper derives a conjectured formula for the leading anomalous dimensions of long double-trace operators in N=4 super Yang-Mills theory at strong coupling, revealing a large residual degeneracy and connecting to supergravity loop corrections.

Contribution

It introduces a new conjecture for the leading anomalous dimensions of all long double-trace operators in the strong coupling regime of N=4 SYM, highlighting their degeneracy and relation to conformal Casimir operators.

Findings

Conjectured a universal formula for anomalous dimensions.

Identified a large residual degeneracy in the spectrum.

Linked anomalous dimensions to supergravity loop discontinuities.

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.