Large Charge Jets in $\mathcal{N}=4$ SYM Energy Correlators

Abstract

We compute the energy-energy correlator in a state created by a heavy canonical operator of scaling dimension ${\Delta }_H$ in $\mathcal{N}=4$ $SU(N)$ SYM, at fixed $N$ and arbitrary values of the large charge 't Hooft coupling $\lambda \sim {\Delta }_H{g}_{\mathrm{YM}}^2$. The state created by the canonical operator triggers spontaneous breaking of conformal symmetry and the Higgs mechanism, with squared W-boson masses proportional to $\lambda$. We start with the known finite-coupling result for the underlying four-point function of local operators, perform the detector and Fourier transforms and express the resulting energy-energy correlator as an infinite OPE sum in the source-detector channel, which we then analyze both numerically and analytically. We show that the finite-coupling energy-energy correlator exhibits a hierarchy of distinct physical regimes as a function of $z=(1-\cos \theta )/2$, where $\theta$ is the angle between the detectors. A small-angle vacuum-dominated behavior at $z\ll {\lambda }^{-1}$ is followed by a non-monotonic medium-induced transient behavior at $\lambda z\sim 1$. A large charge jet regime follows, where the energy-energy correlator displays a power-law behavior $\sim 1/(\lambda z^3)$ for ${\lambda }^{-1}\lesssim z\lesssim {\lambda }^{-1/3}$, before approaching an angle-independent plateau at larger angles.

66 pages, 9 figures