Perturbative and non-perturbative partial supersymmetry breaking: N = 4 → N = 2 → N = 1

We show the existence of a supersymmetry breaking mechanism in string theory, where N = 4 supersymmetry is broken spontaneously to N = 2 and N = 1 with moduli-dependent gravitino masses. The spectrum of the spontaneously broken theory with lower supersymmetry is in one-to-one correspondence with the spectrum of the heterotic N = 4 string. The mass splitting of the N = 4 spectrum depends on the compactification moduli as well as the three R-symmetry charges. We also show that, in string theory, chiral theories can be obtained after spontaneous breaking of extended supersymmetry. This was impossible at the level of field theory. In the large-moduli limit a restoration of the N = 4 supersymmetry is obtained. As expected the graviphotons and some of the gauge bosons become massive in N = 1 vacua. At some special points of the moduli space some of the N = 4 states with non-zero winding numbers and with spin 0 and 12 become massless chiral superfields of the unbroken N = 1 supersymmetry. Such vacua have a dual type II description, in which there are magnetically charged states with spin 0 and 12 that become massless. The heterotic-type II duality suggests some novel non-perturbative transitions on the type II side. Such transitions do not seem to have a geometric interpretation, since they relate type II vacua with symmetric world-sheet structure to asymmetric ones. The heterotic interpretation of such a transition is an ordinary Higgsing of an SU(2) factor. In the case of N = 4 → N = 2, the perturbative N = 2 prepotential is determined by the perturbative N = 4 BPS states. This observation permits us to suggest a method to determine the exact non-perturbative prepotential of the effective N = 2 supergravity using the shifted spectrum of the non-perturbative BPS states of the underlying N = 4 theory.