A linear equation for Wilson loops

The Makeenko–Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD₂ it is possible to reformulate this equation as a linear equation with second order derivatives. This equation is a bound state Schrödinger equation with a three-dimensional Coulomb potential. Thus, loop dynamics leads to a surprising new picture of confinement, where this phenomenon is due to a (bound state) localization in loop space, with the Wilson loops decaying exponentially outside a characteristic radius.