An exact slope for AdS/CFT

TL;DR

This paper conjectures an exact formula for the minimal scaling dimension of Wilson operators in N=4 SYM in the small spin limit, valid across all coupling regimes, supported by weak and strong coupling evidence.

Contribution

It provides a closed-form conjecture for the small spin limit of operator dimensions in AdS/CFT, extending the understanding of the spectrum in planar N=4 SYM.

Findings

Agreement with one-loop string energy spectra at strong coupling

Evidence from weak and strong coupling supports the conjecture

Formula derived from the asymptotic Bethe Ansatz equations

Abstract

We present a conjecture for the small spin limit of the minimal scaling dimension of Wilson operators in the sl(2) sector of the planar N=4 Super-Yang-Mills theory. The expression is given in closed form as a function of the 't Hooft coupling and twist of the operator. The formula should stand as a prediction of the Asymptotic Bethe Ansatz equations for the spectrum of scaling dimensions and evidence is given at both weak and strong coupling that it should be exact. In particular, agreement is found with established one-loop spectroscopy of string energies at strong coupling.