# University of Hertfordshire

## Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy

Research output: Contribution to journalArticle

### Documents

Original language English 63 34 JHEP 2016 11 10 Nov 2016 https://doi.org/10.1007/JHEP11(2016)063 E-pub ahead of print - 10 Nov 2016

### Abstract

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.