M-theory on G2-manifolds


String theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics




The Kaluza-Klein reduction of 11-dimensional supergravity on G2 manifolds yields an effective N=1N=1 4-dimensional supergravity. This construction is the lift to M-theory of the KK-compactification of string theory on Calabi-Yau manifolds.

Specifically for discussion of obtaining or approximating the standard model of particle physics by this procedure see at G2-MSSM.


The C-field

In compactifications with weak G2 holonomy it is the defining 4-form ϕ 4\phi_4 (the one which for strict G2 manifolds is the Hodge dual of the associative 3-form) which is the flux/field strength of the supergravity C-field. See for instance towards the end of (Bilal-Serendinger-Sfetos) for a derivation.


For realistic field content after Kaluza-Klein compactification one needs to consider not smooth (weak) G2-manifolds but orbifolds of these. see the first page of (Acharya-Denef-Hofman-Lambert) for discussion of phenomenology for such orbifold G 2G_2 models and further pointers and see (Achary 98) for general discussion of orbifolds with G 2G_2-structure.


Discussion of Freund-Rubin compactification on 4×X 7\mathbb{R}^4 \times X_7 “with flux”, hence non-vanishing supergravity C-field and how they preserve one supersymmetry if X 7X_7 is of weak G2 holonomy with λ\lambda = cosmological constant = C-field strength on 4\mathbb{R}^4 is in

  • Adel Bilal, J.-P. Derendinger, K. Sfetsos, (Weak) G 2G_2 Holonomy from Self-duality, Flux and Supersymmetry, Nucl.Phys. B628 (2002) 112-132 (arXiv:hep-th/0111274)

Surveys include

  • Mike Duff, M-theory on manifolds of G2 holonomy: the first twenty years (arXiv:hep-th/0201062)

  • Sergei Gukov, M-theory on manifolds with exceptional holonomy, Fortschr. Phys. 51 (2003), 719–731 (pdf)

  • Bobby Acharya, M Theory, G 2G_2-manifolds and Four Dimensional Physics, Classical and Quantum Gravity Volume 19 Number 22 (pdf)

  • Thomas House, Andrei Micu, M-theory Compactifications on Manifolds with G 2G_2 Structure (arXiv:hep-th/0412006)

  • Adil Belhaj, M-theory on G2 manifolds and the method of (p, q) brane webs (2004) (web)

Compactificaton on orbifolds of G 2G_2-manifolds, introducing (orbifold-) singularities necessary for realistic effective QFTs is discussed in

The corresponding membrane instanton corrections to the superpotential? are discussed in

The hierarchy problem in the context of G 2G_2-compactifications is discussed in

A survey of the corresponding string phenomenology is in

  • Bobby Acharya, G 2G_2-manifolds at the CERN Large Hadron collider and in the Galaxy, talk at G 2G_2-days (2012) (pdf)

Revised on January 11, 2013 20:26:15 by Urs Schreiber (