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 $\lambda \sim \Delta_H g_{\rm YM}^2$. 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 $\lambda z \sim1$. A large charge jet regime follows, where the energy-energy correlator displays a power-law behavior $\sim1/(\lambda z^3)$ for $\lambda^{-1}\lesssim z \lesssim \lambda^{-1/3}$, before approaching an angle-independent plateau at larger angles.