Monopole condensates in Seiberg-Witten theory

A product of two Riemann surfaces of genuses p1 and p2 solves the Seiberg-Witten monopole equations for a constant Weyl spinor that represents a monopole condensate. Self-dual electromagnetic fields require p1=p2=p and provide a solution of the euclidean Einstein-Maxwell-Dirac equations with p−1 magnetic vortices in one surface and the same number of electric vortices in the other. The monopole condensate plays the role of cosmological constant. The virtual dimension of the moduli space is zero, showing that for given p1 and p2, the solutions are unique.