On the geometry underlying supersymmetric flux vacua with intermediate SU(2) structure

TL;DR

This paper explores the geometric structures underlying supersymmetric flux vacua with intermediate SU(2) structure, linking them to special half-flat structures and constructing new solutions from various geometric manifolds.

Contribution

It establishes a connection between supersymmetric flux vacua and specific half-flat structures, and constructs new solutions using hyperk"ahler, hypo, and solvmanifolds.

Findings

Solutions of SUSY IIA have symplectic half-flat structures.

Solutions of SUSY IIB are near balanced half-flat structures.

Compact simply connected manifolds do not admit SUSY IIB solutions.

Abstract

We show that supersymmetric flux vacua with intermediate SU(2) structure is closely related to some special classes of half-flat structures. More concretely, solutions of the SUSY equations IIA possess a symplectic half-flat structure, whereas solutions of the SUSY equations IIB admit a half-flat structure which is in certain sense near to the balanced condition. Using this result we show that compact simply connected manifolds do not admit type IIB solutions. New solutions of the SUSY equations IIA and IIB are constructed from hyperk\"ahler 4-manifolds, special hypo 5-manifolds and 6-dimensional solvmanifolds.