Forgot to change title.

]]>Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Added multiple redirects at the bottom of the page.)

]]>pointer to

- Sergei Gukov.
*Solitons, Superpotentials and Calibrations*. Nuclear Physics B Volume 574, Issues 1–2, 15 May 2000, Pages 169-188. (doi)

added pointer to today’s:

- Eric Gonzalez, Gordon Kane, Khoa Dang Nguyen, Malcolm Perry,
*Quark and lepton mass matrices from localization in M-theory on $G_2$ orbifold*(arXiv:2002.11820)

added pointer to today’s:

- Bobby Acharya, Lorenzo Foscolo, Marwan Najjar, Eirik Eik Svanes,
*New $G_2$-conifolds in M-theory and their Field Theory Interpretation*(arXiv:2011.06998)

added these original references:

M. A. Awada, Mike Duff, Christopher Pope,

*$N=8$ Supergravity Breaks Down to $N=1$*, Phys. Rev. Lett. 50, 294 (1983) (doi:10.1103/PhysRevLett.50.294)Mike Duff, Bengt Nilsson, Christopher Pope,

*Spontaneous Supersymmetry Breaking by the Squashed Seven-Sphere*, Phys. Rev. Lett. 50, 2043 (1983) (doi:10.1103/PhysRevLett.50.2043, erratum)(compactification on a squashed 7-sphere with $G_2$-holonomy)

added pointer to today’s

- Max Hubner,
*Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics*(arXiv:2009.07136)

added pointer to

- Andreas Braun, Sebastjan Cizel, Max Hubner, Sakura Schafer-Nameki,
*Higgs Bundles for M-theory on G2-Manifolds*(arXiv:1812.06072)

added pointer to

- Andreas Braun, Sakura Schaefer-Nameki,
*Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality*, JHEP04(2018)126 (arXiv:1708.07215)

will add this also to *heterotic string theory on CY3-manifolds*

added pointer to

- Jacob L. Bourjaily, Sam Espahbodi,
*Geometrically Engineerable Chiral Matter in M-Theory*(arXiv:0804.1132)

replaced illustration of blowup of ADE-singularity by a better graphics (here)

]]>further added a paragraph *Nonabelian gauge groups and chiral fermions at orbifold singularities*. Am splitting off an entry *enhanced gauge symmetry* now.

added a paragraph on $\tau \coloneqq C_3 + i \phi_3$ being the complexified modulus of $G_2$ KK-compactification, and added pointers to a few relevant references, here

]]>The discussion of which compactification spaces to take, locally, to get the desired $N=1$ SYM goes back to Acharya 98. More details are in Atiyah-Witten 01, see specifically section 6 there.

]]>Underlying all this is the claim/assumption that one may find a KK-compactification reducing to a globally $N=1$-supersymmetric extension of the standard model at the electroweak scale at all. This “fixes”, by construction, the species of sparticles, as being the superpartners of the experimentally observed particles. Given this, the remaining question is which masses they have, and it is these that is here being claimed to be all controled by just one compactification parameter.

The compactification itself is in these articles discussed locally in the fiber space only. The fiber space needs to be, apart from having $G_2$-holonomy, an orbifold with certain stabilizer group that encodes the nonabelian gauge group of the resulting effective model. One hopes that for the relevant choices there are globalizations of this to compact orbifolds, see for instance the second but last paragraph on p. 34 of arXiv:0801.0478.

]]>In the abstract of

Sebastian A.R. Ellis, Gordon L. Kane, Bob Zheng

Superpartners at LHC and Future Colliders: Predictions from Constrained Compactified M-Theoryhttp://arxiv.org/abs/1408.1961

they mention

Within this framework the discovery of a single sparticle is sufficient to determine uniquely the SUSY spectrum,

Does that mean that all the superpartner masses can be/are given in terms of a single such mass? Or is it more of determining what superparticles there are?

]]>Added to *M-theory on G2-manifolds* some minimum remarks under *Vacuum solutions and torsion constraints*, added more of the original articles to the list of references, added more recent references at *G2-MSSM*, re-organized the section outline slightly at *torsion constraints in supergravity* and cross-linked these entries a bit more.

under *Details* I have added two elementary remarks on how two identify $G_2$-compactification structure with physical fields.

(Just so as to record the pointers to the relevant references for the moment.)

]]>added further commented references to *M-theory on G2-manifolds*

started *M-theory on G2-manifolds*