Decomposable $(5,6)$-solutions in eleven-dimensional supergravity

Abstract

We present decomposable (5,6)-solutions ${\tilde{M}}^{1,4}\times M^6$ in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogue of work done by I. Chrysikos and A. Galaev who made similar computations for decomposable (6,5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with negative Einstein constant (in the "mostly plus" convention) and Riemannian Kähler-Einstein manifolds with positive Einstein constant. This conclusion generalizes a result of C. N. Pope and P. van Nieuwenhuizen concerning the appearance of six-dimensional Kähler-Einstein manifolds in eleven-dimensional supergravity. In this setting we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein-Sasakian structures with negative Einstein constant on the 5-sphere, known from the work of C. P. Boyer et al.

arXiv commentAccepted manuscript, 30 pages

References in corpus (33)

• String Theory Dynamics In Various Dimensions
• M-Theory on Eight-Manifolds
• The Geometry of D=11 Killing Spinors
• Supersymmetric AdS_5 solutions of M-theory
• Compactification of D=11 supergravity on spaces of exceptional holonomy
• On Eta-Einstein Sasakian Geometry
• G-Structures, Fluxes and Calibrations in M-Theory
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
• Breaking the M-waves
• (Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry
• Metrics With Vanishing Quantum Corrections
• New Kaluza-Klein Instantons and Decay of AdS Vacua
• M-theory Compactifications on Manifolds with G2 Structure
• Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
• M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures
• Supersymmetry of AdS and flat backgrounds in M-theory
• The homogeneity theorem for supergravity backgrounds
• Screen bundles of Lorentzian manifolds and some generalisations of pp-waves
• Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
• Supersymmetry, holonomy and Kundt spacetimes
• Unit Killing Vector Fields on Nearly Kahler Manifolds
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• Lorentzian symmetric spaces in supergravity
• Holonomy groups of Lorentzian manifolds
• Killing superalgebras for Lorentzian six-manifolds
• Holonomy of Einstein Lorentzian manifolds
• Symmetric M-Theory Backgrounds
• The field and Killing spinor equations of M-theory and type IIA/IIB supergravity in coordinate-free notation
• Killing superalgebras for lorentzian five-manifolds
• A Geometric Construction of Solutions to 11D Supergravity
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• Sasakian manifolds and M-theory
• Decomposable (6, 5)-solutions in eleven-dimensional supergravity