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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 14th 2012
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 4th 2013

added further commented references to M-theory on G2-manifolds

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 11th 2013

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.)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 29th 2015
• (edited Jan 29th 2015)

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.

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeJan 29th 2015

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?

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJan 29th 2015
• (edited Jan 29th 2015)

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.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJan 29th 2015

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.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 22nd 2015
• (edited May 22nd 2015)

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

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 23rd 2015
• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 17th 2018

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

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeAug 16th 2018

• Jacob L. Bourjaily, Sam Espahbodi, Geometrically Engineerable Chiral Matter in M-Theory (arXiv:0804.1132)
• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMar 25th 2019
• (edited Mar 25th 2019)

• 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

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJul 9th 2019

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeSep 16th 2020

added pointer to today’s

• Max Hubner, Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics (arXiv:2009.07136)
• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeOct 15th 2020

added these original references:

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeNov 16th 2020

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)
• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeFeb 2nd 2021

added pointer to today’s: