Light-front diagnostics in the 't Hooft model: I. Wave functions, EMT trace decomposition, and Coulomb energy

Abstract: We use the large-$N_c$ 't Hooft model to build a state-by-state light-front map connecting meson wave functions, momentum distributions, Coulomb/confinement energy, EMT trace decomposition, forward GPD moments, and momentum-space entropy. Light-light states develop broad longitudinal momentum distributions and rapidly become Coulomb/confinement dominated, while heavy-heavy states remain localized near equal momentum sharing and retain a large quark-mass component. In the light-front momentum-fraction representation, the bilocal Coulomb kernel is sign-changing and is not a positive one-body density. The construction provides a controlled $1{+}1$-dimensional light-front setting for separating wave-function, interaction-energy, forward GPD-moment, and EMT information without transverse geometry.