M-theory on manifolds of G2 holonomy: the first twenty years

Abstract

In 1981, covariantly constant spinors were introduced into Kaluza-Klein theory as a way of counting the number of supersymmetries surviving compactification. These are related to the holonomy group of the compactifying manifold. The first non-trivial example was provided in 1982 by D=11 supergravity on the squashed S7, whose G2 holonomy yields N=1 in D=4. In 1983, another example was provided by D=11 supergravity on K3, whose SU(2) holonomy yields half the maximum supersymmetry. In 2002, G2 and K3 manifolds continue to feature prominently in the full D=11 M-theory and its dualities. In particular, singular G2 compactifications can yield chiral (N=1,D=4) models with realistic gauge groups. The notion of generalized holonomy is also discussed.

Notes added on n, the number of allowed M-theory supersymmetries. Asymmetric orbifold compactifications of Type II strings from D=10 to D=2 permit n=0,1,2,3,4,5,6,8,9,10,12,16,17,18,20,24,32

References in corpus (8)

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• pp-waves in 11-dimensions with extra supersymmetry
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• A New Fractional D2-brane, G_2 Holonomy and T-duality
• Generalized holonomy of M-theory vacua
• Spin(9)-structures and connections with totally skew-symmetric torsion

Cited by in corpus (33)

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• N=31, D=11
• Fourteen new stationary points in the scalar potential of SO(8)-gauged N=8, D=4 supergravity
• IIB solutions with N>28 Killing spinors are maximally supersymmetric
• Generalized holonomy of M-theory vacua
• M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
• G_2 Domain Walls in M-theory
• Duality and cohomology in M-theory with boundary
• Killing spinors in supergravity with 4-fluxes
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• Generalized Holonomy of Supergravities with 8 Real Supercharges
• Higher Order Integrability in Generalized Holonomy
• Invariant Killing spinors in 11D and type II supergravities
• Supersymmetric geometries of IIA supergravity III
• Hamiltonian structure and noncommutativity in $p$-brane models with exotic supersymmetry
• M-theory compactifications, G_2-manifolds and anomalies
• Erice lectures on "The status of local supersymmetry"
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• Self-dual non-Abelian N = 1 tensor multiplet in D = 2+ 2 dimensions
• Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems
• The Killing spinor equation with higher order potentials
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• Dirac equation on a G_2 manifold
• BPS preons in M-theory and supergravity
• Spin Geometry and Some Applications
• G${}_2$-Manifolds and M-Theory Compactifications
• Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model',12. - 17. July 2003, Portoroz, Slovenia (Part 2 of 2)
• Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles
• M-Theory on Manifolds with G_2 Holonomy