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

TL;DR

This paper demonstrates a string theory mechanism for spontaneous partial supersymmetry breaking from N=4 to N=2 and N=1, revealing moduli-dependent spectra, dualities, and non-perturbative effects.

Contribution

It introduces a novel supersymmetry breaking mechanism in string theory with moduli dependence and explores dualities and non-perturbative transitions affecting the spectrum.

Findings

N=4 supersymmetry can be spontaneously broken to N=2 and N=1 in string theory.

Chiral theories emerge after supersymmetry breaking, unlike in field theory.

The non-perturbative prepotential can be determined from the shifted spectrum of BPS states.

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.