Superpotential from Black Holes

Abstract

BPS monopoles in N=2 SUSY theories may lead to monopole condensation and confinement. We have found that supersymmetric black holes with non-vanishing area of the horizon may stabilize the moduli in theories where the potential is proportional to the square of the graviphoton central charge. In particular, in known models of spontaneous breaking of N=2 to N=1 SUSY theories, the parameters of the electric and magnetic Fayet--Iliopoulos terms can be considered proportional to electric and magnetic charges of the dyonic black holes. Upon such identification the potential is found to be proportional to the square of the black hole mass. The fixed values of the moduli near the black hole horizon correspond exactly to the minimum of this potential. The value of the potential at the minimum is proportional to the black hole entropy.