# Supersymmetric backgrounds, the Killing superalgebra, and generalised special holonomy

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Journal of High Energy Physics

, 2016:63

First Online: 10 November 2016Received: 26 September 2016Accepted: 30 October 2016 Abstract

We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving \ \mathcal{N} \ supersymmetries in dimensions D ≥ 4 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} {dd}\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-Poincaré algebra.

KeywordsDifferential and Algebraic Geometry Flux compactifications Supergravity Models Superstring Vacua ArXiv ePrint: 1606.09304

Autor: André Coimbra - Charles Strickland-Constable