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started M-theory on G2-manifolds
added further commented references to M-theory on G2-manifolds
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 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.
In the abstract of
Sebastian A.R. Ellis, Gordon L. Kane, Bob Zheng Superpartners at LHC and Future Colliders: Predictions from Constrained Compactified M-Theory http://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?
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.
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.
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
further added a paragraph Nonabelian gauge groups and chiral fermions at orbifold singularities. Am splitting off an entry enhanced gauge symmetry now.
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will add this also to heterotic string theory on CY3-manifolds
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