Foliated backgrounds for M-theory compactifications (II)

Abstract

We summarize the foliation approach to $\mathcal{N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to ${\mathrm{AdS}}_3$ spaces for the case when the internal part $\xi$ of the supersymmetry generator is chiral on some proper subset $\mathcal{W}$ of $M$. In this case, a topological no-go theorem implies that the complement $M\setminus \mathcal{W}$ must be a dense open subset, while $M$ admits a singular foliation $\bar{\mathcal{F}}$ (in the sense of Haefliger) which is defined by a closed one-form $\mathbf{\omega }$ and is endowed with a longitudinal $G_2$ structure. The geometry of this foliation is determined by the supersymmetry conditions. We also describe the topology of $\bar{\mathcal{F}}$ in the case when $\mathbf{\omega }$ is a Morse form.

10 pages, conference proceedings -- "Quantum Field Theory and Nonlinear Dynamics", 24-28 September 2014, Sinaia, Romania

References in corpus (4)

• Short-time behaviour of a modified Laplacian coflow of G2-structures
• Geometric algebra techniques in flux compactifications (II)
• Foliated eight-manifolds for M-theory compactification
• Flux Compactification of M-theory on Compact Manifolds with Spin(7) Holonomy