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

TL;DR

The work addresses the problem of determining the leading anomalous dimensions of all long double-trace operators in N=4 SYM at large N and strong coupling. It develops an unmixing framework based on the holographic four-point correlators and long multiplet expansions, linking anomalous dimensions to data encoded in A and M matrices and to Casimir-operator structures. The authors conjecture a general formula for the leading dimensions, demonstrate a Casimir-based approach to compute leading discontinuities at arbitrary loop orders, and validate the conjecture across multiple su(4) channels up to moderate twists. This provides a cohesive route to 1/N^2 and potentially higher-order corrections for holographic correlators and deepens understanding of degeneracies in the double-trace spectrum.

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.

Figures (2)

• Figure 1: A free theory diagram absent from $\langle p_1 p_2 p_3 p_4\rangle$.
• Figure 2: Free theory diagrams in the light-like limit.