Perturbative and Non-Perturbative Partial Supersymmetry Breaking; N=4 -> N=2 -> N=1

TL;DR

This work establishes the existence of spontaneous partial supersymmetry breaking in string theory, showing how $N=4$ can break to $N=2$ and $N=1$ with moduli-dependent gravitino masses, while preserving a one-to-one correspondence with the perturbative heterotic $N=4$ spectrum and enabling chiral $N=1$ sectors not realizable in field theory. It provides concrete constructions via freely acting orbifolds and generalized boosts, analyzes the perturbative and non-perturbative BPS spectra, and demonstrates the restoration of higher supersymmetry in large-moduli limits. The paper also explores heterotic–Type II dualities, including non-geometric and non-perturbative transitions, and outlines a speculative genus-2 framework for non-perturbative BPS multiplicities and the exact non-perturbative prepotential in partially broken phases. Overall, it lays a foundation for understanding how chirality and realistic spectra may emerge from spontaneous breaking of extended SUSY in string theory, with testable implications for dual descriptions and non-perturbative dynamics.

Abstract

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 {1/2} become massless chiral superfields of the unbroken N=1 supersymmetry. Such vaccua have a dual type II description, in which there are magnetically charged states with spin 0 and {1/2} 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 vaccua with symmetric worlsheet structure to assymetric ones. The heteroric 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 let us to suggest a method which determines 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.