Abstract
We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form . Using the language of generalised geometry, we show that, for , preserving minimal supersymmetry is equivalent to the manifold M having generalised special holonomy and list the relevant holonomy groups. We conjecture that this result extends to backgrounds preserving any number of supersymmetries. As a prime example, we consider in D = 4. The corresponding generalised special holonomy group is , giving the natural M theory extension to the notion of a G2 manifold, and, for Type II backgrounds, reformulating the pure spinor conditions as an integrable structure.
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