Energy-energy correlators in the large-charge limit of $\mathcal{N}=4$ super Yang-Mills theory

Abstract

We study the energy-energy correlator (EEC) in heavy states of four-dimensional $\mathcal N=4$ super Yang--Mills theory in the large-charge't Hooft limit, in which the dimension $\Delta$ of the heavy operator (or, equivalently, its $R$-charge) is taken to infinity with the effective coupling $\lambda_Q \propto g_{\mathrm{YM}}^2\Delta$ held fixed. The relevant heavy-heavy-light-light four-point correlators are known to all orders in $\lambda_Q$ in this limit. For certain classes of operators, the perturbative series can be resummed to obtain exact finite-coupling expressions. We use these results to determine the corresponding EEC, whose dynamical part can be extracted from a double discontinuity of the four-point correlator. We determine the EEC at finite effective coupling and study its physical behavior as a function of $\lambda_Q$ and the angular separation between the detectors, both at generic angles and in the collinear and back-to-back limits.