Foliated eight-manifolds for M-theory compactification
arXiv:1411.3148 · doi:10.1007/JHEP01(2015)140
Abstract
We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and torsion classes of the G2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C star algebra of the foliation is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from the four-form field strength, which must satisfy the Latour obstruction. We also give a criterion in terms of this class for when such foliations are fibrations over the circle. When the criterion is not satisfied, each leaf of the foliation is dense in M.
63 pages, 2 figures
References in corpus (34)
- On Flux Quantization In M-Theory And The Effective Action
- Eleven Dimensional Origin of String/String Duality: A One Loop Test
- The Geometry of D=11 Killing Spinors
- G-Structures, Fluxes and Calibrations in M-Theory
- Nonassociative tori and applications to T-duality
- Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds
- The Srni lectures on non-integrable geometries with torsion
- Flows of G_2 Structures, I
- Deformations of G_2 and Spin(7) Structures on Manifolds
- A Note on Compactifications on Spin(7)-Holonomy Manifolds
- 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
- (Non-)commutative closed string on T-dual toroidal backgrounds
- On BPS preons, generalized holonomies and D=11 supergravities
- A note on simple applications of the Killing Spinor Identities
- Polyvector Super-Poincare Algebras
- Short-time behaviour of a modified Laplacian coflow of G2-structures
- Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
- M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures
- Toward the Determination of R^3F^2 Terms in M-theory
- The geometric algebra of Fierz identities in arbitrary dimensions and signatures
- M-theory on Spin(7) Manifolds, Fluxes and 3D, N=1 Supergravity
- Higher-derivative gauge field terms in the M-theory action
- Geometric algebra techniques in flux compactifications (II)
- T-duality revisited
- Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds
- Local geometry of the G2 moduli space
- New potentials from Scherk-Schwarz reductions
- Geometric algebra techniques in flux compactifications
- Spin(7)-manifolds in compactifications to four dimensions
- Killing spinors in supergravity with 4-fluxes
- Generalized curvature and the equations of D=11 supergravity
- Flux Compactification of M-theory on Compact Manifolds with Spin(7) Holonomy
- Spin(7)-manifolds with parallel torsion form
- The Killing spinor equation with higher order potentials
Cited by in corpus (13)
- Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
- On supersymmetric AdS solutions of Type II
- Generalised Structures for AdS Backgrounds
- Geometric algebra techniques in flux compactifications
- AdS Solutions of M-theory
- M-theory on non-Kähler manifolds
- Spinors of real type as polyforms and the generalized Killing equation
- Foliated backgrounds for M-theory compactifications (II)
- Choices of spinor inner products on M-theory backgrounds
- A class of non-geometric M-theory compactification backgrounds
- Foliated backgrounds for M-theory compactifications (I)
- Five-dimensional null & time-like supersymmetric geometries
- Singular foliations for M-theory compactification