Monopole condensates in Seiberg-Witten theory

A product of two Riemann surfaces of genuses p(1) and p(2) solves the Seiberg-Witten monopole equations for a constant Weyl spinor that represents a monopole condensate. Self-dual electromagnetic fields require p(1) = p(2) = 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 p(1) and P-2, the solutions are unique. (C) 1999 Published by Elsevier Science B.V. All rights reserved.