# Supersymmetric Backgrounds and Generalised Special Holonomy

André Coimbra, Charles Strickland-Constable, Daniel Waldram

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

## 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 $\mathbb{R}^{D-1,1}\times M$. Using the language of $E_{d(d)}\times\mathbb{R}^+$ generalised geometry, we show that, for $D\geq 4$, 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 $\mathcal{N}=1$ in $D=4$. The corresponding generalised special holonomy group is $SU(7)$, giving the natural M theory extension to the notion of a $G_2$ manifold, and, for Type II backgrounds, reformulating the pure spinor $SU(3)\times SU(3)$ conditions as an integrable structure.
Original language Undefined/Unknown 27 Classical and Quantum Gravity 33 12 https://doi.org/10.1088/0264-9381/33/12/125026 Published - 20 May 2016

• hep-th
• math.DG