Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds

A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus corresponds to a constant curvature connection. On a noncommutative toroidal orbifold there is an additional constraint that the connection be equivariant. We study moduli spaces of (equivariant) constant curvature connections on noncommutative even-dimensional tori and on toroidal orbifolds. As an illustration we work out the cases of Z2 and Z4 orbifolds in detail. The results we obtain agree with a commutative picture describing systems of branes wrapped on cycles of the torus and branes stuck at exceptional orbifold points.