Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy

Abstract

We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving $\mathcal{N}$ supersymmetries in dimensions $D\ge 4$ 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 $E_{d(d)}\times {\mathbb{R}}^{+}$ 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-Poincaré algebra.

34 pages

References in corpus (11)

• Generalised Geometry for M-Theory
• Generalized complex geometry
• AdS_6 solutions of type II supergravity
• Holonomy and Symmetry in M-theory
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• Supersymmetry of AdS and flat backgrounds in M-theory
• Supersymmetry of AdS and flat IIB backgrounds
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• AdS_4 compactifications of AdS_7 solutions in type II supergravity
• On the maximal superalgebras of supersymmetric backgrounds
• New gaugings and non-geometry

Cited by in corpus (5)

• Half-maximal supersymmetry from exceptional field theory
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• Supersymmetric AdS backgrounds and weak generalised holonomy
• Classical worldvolumes as generalised geodesics
• Brane current algebras and generalised geometry from QP manifolds