Geometry of type II common sector N=2 backgrounds

Abstract

We describe the geometry of all type II common sector backgrounds with two supersymmetries. In particular, we determine the spacetime geometry of those supersymmetric backgrounds for which each copy of the Killing spinor equations admits a Killing spinor. The stability subgroups of both Killing spinors are $Spin(7)\ltimes \bR^8$, $SU(4)\ltimes \bR^8$ and $G_2$ for IIB backgrounds, and $Spin(7)$, SU(4) and $G_2\ltimes \bR^8$ for IIA backgrounds. We show that the spacetime of backgrounds with spinors that have stability subgroup $K\ltimes \bR^8$ is a pp-wave propagating in an eight-dimensional manifold with a $K$-structure. The spacetime of backgrounds with $K$-invariant Killing spinors is a fibre bundle with fibre spanned by the orbits of two commuting null Killing vector fields and base space an eight-dimensional manifold which admits a $K$-structure. Type II T-duality interchanges the backgrounds with $K$- and $K\ltimes\bR^8$-invariant Killing spinors. We show that the geometries of the base space of the fibre bundle and the corresponding space in which the pp-wave propagates are the same. The conformal symmetry of the world-sheet action of type II strings propagating in these N=2 backgrounds can always be fixed in the light-cone gauge.

30 pages

References in corpus (19)

• Duality in the Type--II Superstring Effective Action
• Non-Kaehler String Backgrounds and their Five Torsion Classes
• Superstrings with Intrinsic Torsion
• G-Structures and Wrapped NS5-Branes
• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• Twistor spaces for HKT manifolds
• Complex geometry of conifolds and 5-brane wrapped on 2-sphere
• Geometry of Hyper-Kähler Connections with Torsion
• Vanishing Theorems and String Backgrounds
• The spinorial geometry of supersymmetric backgrounds
• Breaking the M-waves
• A no-go theorem for string warped compactifications
• The spinorial geometry of supersymmetric heterotic string backgrounds
• Holonomy groups and W-symmetries
• Systematics of M-theory spinorial geometry
• Twistor Spaces for QKT Manifolds
• Systematics of IIB spinorial geometry
• Potentials for (p,0) and (1,1) supersymmetric sigma models with torsion
• Anomaly, Fluxes and (2,0) Heterotic-String Compactifications

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• Killing-Yano tensors and some applications
• Supersymmetric heterotic string backgrounds
• Killing-Yano equations and G-structures
• Classification, geometry and applications of supersymmetric backgrounds
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• IIB backgrounds with five-form flux
• Supersymmetric geometries of IIA supergravity I
• Supersymmetric geometries of IIA supergravity III