  We show that the massive Yang--Mills action having as a mass term the
non-local operator introduced by Gubarov, Stodolsky, and Zakharov is
classically equivalent to a principal gauged sigma model. The non-local mass
corresponds to the topological term of the sigma model. The latter is obtained
once the degrees of freedom implicitly generated in the non-local action are
explicitly implemented as group elements. The non-local action is recovered by
integrating out these group elements. In contrast to the usual gauge-fixed
treatment, the sigma model point of view provides a safe framework in which
calculation are tractable while keeping a full control of gauge-invariance. It
shows that the non-local massive Yang--Mills action is naturally associated
with the low-energy description of QCD in the Chiral Perturbation Theory
approach. Moreover, the sigma model admits solutions called center vortices
familiar in different (de)-confinement and chiral symmetry breaking scenarios.
This suggests that the non-local operator introduced by Gubarov, Stodolsky, and
Zakharov might be sensitive to center vortices configurations.
