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.

arXiv comment34 pages

References in corpus (56)

• Supergravity description of field theories on curved manifolds and a no go theorem
• Generalised Geometry for M-Theory
• The Geometry of D=11 Killing Spinors
• Generalized structures of N=1 vacua
• G-Structures and Wrapped NS5-Branes
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• On Lagrangians and Gaugings of Maximal Supergravities
• Supergravity as Generalised Geometry I: Type II Theories
• M-theory, exceptional generalised geometry and superpotentials
• N=3 Warped Compactifications
• A scan for new N=1 vacua on twisted tori
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• All AdS_7 solutions of type II supergravity
• Exactly Marginal Deformations and Global Symmetries
• Generalized complex geometry
• G-Structures, Fluxes and Calibrations in M-Theory
• AdS_6 solutions of type II supergravity
• Generalised geometry for string corrections
• Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
• Torsion-free generalized connections and Heterotic Supergravity
• A no-go theorem for string warped compactifications
• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• Holonomy and Symmetry in M-theory
• Supersymmetry and homogeneity of M-theory backgrounds
• Algebroids, Heterotic Moduli Spaces and the Strominger System
• Leibniz algebroids, twistings and exceptional generalized geometry
• The exceptional story of massive IIA supergravity
• Exceptional generalised geometry for massive IIA and consistent reductions
• The Killing superalgebra of ten-dimensional supergravity backgrounds
• E7(7) formulation of N=2 backgrounds
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• N=2 supersymmetric AdS_4 solutions of M-theory
• Gauging Maximal Supergravities
• New supersymmetric flux vacua with intermediate SU(2) structure
• Supersymmetric Backgrounds and Generalised Special Holonomy
• Supersymmetry of AdS and flat backgrounds in M-theory
• AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry
• The homogeneity theorem for supergravity backgrounds
• Exactly marginal deformations from exceptional generalised geometry
• N=1 vacua in Exceptional Generalized Geometry
• Supersymmetry of AdS and flat IIB backgrounds
• On the geometry and the moduli space of beta-deformed quiver gauge theories
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• Symmetric backgrounds of type IIB supergravity
• N=2 vacua in Generalized Geometry
• AdS${}_8$ Solutions in Type II Supergravity
• AdS_4 compactifications of AdS_7 solutions in type II supergravity
• Supersymmetry of IIA warped flux AdS and flat backgrounds
• Bn-generalized geometry and G2(2)-structures
• On the maximal superalgebras of supersymmetric backgrounds
• New gaugings and non-geometry
• Lie algebra of conformal Killing-Yano forms
• Generalized geometric vacua with eight supercharges
• The homogeneity theorem for supergravity backgrounds II: the six-dimensional theories
• Symmetric M-Theory Backgrounds

Cited by in corpus (17)

• Half-maximal supersymmetry from exceptional field theory
• Systematics of consistent truncations from generalised geometry
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• On supersymmetric E11 exceptional field theory
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Generalised Structures for $\mathcal{N}=1$ AdS Backgrounds
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Supersymmetric AdS backgrounds and weak generalised holonomy
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory
• Classical worldvolumes as generalised geodesics
• Spinors of real type as polyforms and the generalized Killing equation
• Generalised holonomies and K(E${}_9$)
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Supergravity Fluxes and Generalised Geometry
• Brane current algebras and generalised geometry from QP manifolds