Generalized Geometry and Partial Supersymmetry Breaking

TL;DR

This review explores the use of generalized geometry in string compactifications, analyzes conditions for stable N=1 vacua in supergravity, and connects these findings to string theory realizations.

Contribution

It provides a comprehensive analysis of SU(2)xSU(2) structures, scalar manifolds, and conditions for partial supersymmetry breaking in supergravity.

Findings

Derived scalar field spaces for SU(2)xSU(2) structures.

Established conditions for stable Minkowski and AdS N=1 vacua.

Connected supergravity solutions to string theory realizations.

Abstract

This review article consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2)xSU(2)-structure compactifications. We show that in contrast to SU(3)xSU(3) structures, there is no dynamical SU(2)xSU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N=4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N=1 vacua in spontaneously broken gauged N=2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N=1 supergravity. We then apply the discussion to special quaternionic-Kahler geometries which appear in the low-energy limit of SU(3)xSU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions.