N=2 vacua in Generalized Geometry

TL;DR

This paper characterizes the conditions for N=2 supersymmetric vacua in type IIA string theory compactifications using Exceptional Generalized Geometry and Generalized Complex Geometry, revealing geometric structures and flux conditions.

Contribution

It formulates the supersymmetry conditions in EGG and GCG frameworks, identifying algebraic structures and closure conditions necessary for N=2 vacua.

Findings

Identifies SU(2)_R structures encoding scalar fields.

Derives flux-twisted closure conditions for these structures.

Provides GCG equations for pure spinors related to supersymmetry.

Abstract

We find the conditions on compactifications of type IIA to four-dimensional Minkowski space to preserve N=2 supersymmetry in the language of Exceptional Generalized Geometry (EGG) and Generalized Complex Geometry (GCG). In EGG, off-shell N =2 supersymmetry requires the existence of a pair of SU(2)_R singlet and triplet algebraic structures on the exceptional generalized tangent space that encode all the scalars (NS-NS and R-R) in vector and hypermultiplets respectively. We show that on shell N=2 requires, except for a single component, these structures to be closed under a derivative twisted by the NS-NS and R-R fluxes. We also derive the corresponding GCG-type equations for the two pairs of pure spinors that build up these structures.