Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy

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We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving $\mathcal{N}$ supersymmetries in dimensions $D\geq4$ correspond precisely to integrable generalised $G_{\mathcal{N}}$ structures, where $G_{\mathcal{N}}$ is the generalised structure group defined by the Killing spinors. In other words, they are the analogues of special holonomy manifolds in $E_{d(d)} \times\mathbb{R}^+$ generalised geometry. In establishing this result, we introduce the Kosmann-Dorfman bracket, a generalisation of Kosmann's Lie derivative of spinors. This allows us to write down the internal sector of the Killing superalgebra, which takes a rather simple form and whose closure is the key step in proving the main result. In addition, we find that the eleven-dimensional Killing superalgebra of these backgrounds is necessarily the supertranslational part of the $\mathcal{N}$-extended super-Poincar\'e algebra.
Original languageEnglish
Article number63
Number of pages34
JournalJournal of High Energy Physics (JHEP)
Issue number11
Early online date10 Nov 2016
Publication statusE-pub ahead of print - 10 Nov 2016


  • hep-th
  • math.DG


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