Abstract: By taking an effective approach, the soft sector of Yang-Mills theory can be described by a topological BF model defined at null infinity. The incorporation of physical boundary conditions on the fields at the future and the past of I enables a holographic reduction that produces a principal chiral lagrangian in two dimensions coupled to an external source. It is then shown that the equations of motion of this model determine the color memory effect. This effect refers to the relative color rotation between two particles that have experienced the presence of a non-abelian flux.