2014/11/20 by André Coimbra, Charles Strickland-Constable, Daniel Waldram · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.DG
paper · pdf · doi:10.1088/0264-9381/33/12/125026
33 pages
arxiv created 2014/11/20 · arxiv updated 2016/07/07
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 ℝD-1,1× M. Using the language of Ed(d)×ℝ+ generalised geometry, we show that, for D≥ 4, 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 N=1 in D=4. The corresponding generalised special holonomy group is SU(7), giving the natural M theory extension to the notion of a G2 manifold, and, for Type II backgrounds, reformulating the pure spinor SU(3)× SU(3) conditions as an integrable structure.