Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory

QCD(2) with fermions in the adjoint representation is invariant under SU(N)/Z(N) and thereby is endowed with a nontrivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same nontrivial structure. When the (Euclidean) space-time is compacted on a sphere S-2, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of ic-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompacted, a k-sector can be mimicked by the presence of k-fundamental charges at infinity, according to Witten's suggestion. However, this property does not hold before decompaction or for the genuine perturbative solution which corresponds to the zero-instanton contribution on S-2.