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

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

2010-07-09

arxiv.org/abs/1007.1578v2

Class.Quant.Grav.28:075004,2011

Mathematics

Differential Geometry

21 pages; to be published in Classical Quantum Gravity

Scientific paper

10.1088/0264-9381/28/7/075004

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.

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