Walls of marginal stability and dyon spectrum in N=4 supersymmetric string theories

The spectrum of quarter BPS dyons in N = 4 supersymmetric string theories can change as the asymptotic moduli cross walls of marginal stability on which the dyon can break apart in to a pair of half BPS states. In this paper we classify these marginal stability walls and examine this phenomenon in the context of exact dyon spectrum found in a class of N = 4 supersymmetric string theories. We argue that the dyon partition functions in different domains separated by marginal stability walls are the same, but the choice of integration contour needed for extracting the degeneracies from the partition function differ in these different regions. We also find that in the limit of large charges the change in the degeneracy is exponentially suppresed compared to the leading contribution. This is consistent with the fact that in the computation of black hole entropy we do not encounter any change as the asymptotic modulifields move across the walls of marginal stability. Finally we carry out some tests of S-duality invariance in the theory.