Generalised $G_2$-structures and type IIB superstrings

Abstract

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group $SO(d,d)$ of the vector bundle $T^d\oplus T^{d\ast }$ to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7-manifolds with two covariantly constant spinors leads to a generalised $G_2$-structure associated with a reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU(3)-structure associated with $SU(3)\times SU(3)$, and show how these relate to generalised $G_2$-structures.

14 pages, v2: Section 4 rewritten and references added, final version of the paper to appear in JHEP

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• Superstrings with Intrinsic Torsion
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• The Hitchin functionals and the topological B-model at one loop
• Generalised $G_2$-manifolds
• Special metric structures and closed forms
• Mirror symmetry for topological sigma models with generalized Kahler geometry

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