We use a combination of perturbation theory, holography, supersymmetric localization, integrability, and numerical conformal bootstrap methods to constrain the energy-energy correlator in \text{SU}(N_c) {\mathcal N}=4 SYM at finite coupling. For finite N_c, we derive lower bounds on the second and fourth multipoles of the energy-energy correlator at different couplings, along with a smeared energy-energy correlator as a function of the angle between the two detectors. We present evidence that our lower bounds on the multipoles are nearly saturated by the {\mathcal N}=4 SYM theory. In the planar limit, we further use dispersive functionals to obtain tight two-sided bounds on both the first three non-trivial multipoles and on the angular dependence of the energy-energy correlator. As the coupling is varied from weak to strong, the energy-energy correlator exhibits a transition from single-trace to double-trace operator dominance in the collinear limit, which we characterize quantitatively. A similar phenomenon occurs in QCD, where a parton-hadron transition is observed as detectors are brought closer together.
