Conformal collider bootstrap in ${\mathcal N}=4$ SYM

TL;DR

This paper combines multiple advanced theoretical and numerical methods to analyze the energy-energy correlator in ${ m SU}(N_c)$ ${ m extbf{N}=4}$ SYM at various couplings, revealing bounds and a transition in operator dominance.

Contribution

It introduces new bounds on energy-energy correlator multipoles in ${ m N}=4$ SYM at finite and large N, and characterizes a coupling-dependent transition in operator dominance.

Findings

Lower bounds on multipoles are nearly saturated by ${ m N}=4$ SYM.

Tight two-sided bounds on multipoles in the planar limit.

Identification of a transition from single-trace to double-trace dominance with coupling variation.

Abstract

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 ${\cal N} = 4$ 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.