Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory

TL;DR

This paper investigates the conditions for spontaneous N=2 to N=1 supersymmetry breaking in supergravity and string theory, highlighting the role of charged multiplets, special geometries, and fluxes in stable vacua.

Contribution

It provides the general conditions for N=1 vacua in N=2 supergravities using the embedding tensor formalism, including the necessity of charged multiplets and specific geometric conditions.

Findings

N=1 vacua require both electric and magnetic charges.

Stable Minkowski vacua need non-geometric fluxes in string theory.

Results are applicable even with instanton corrections.

Abstract

Using the embedding tensor formalism we give the general conditions for the existence of N=1 vacua in spontaneously broken N=2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kahler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kahler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS N=1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the N=1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.