In "M-theory on manifolds of $G_2$ holonomy: the first twenty years" by Duff, it is claimed (e.g. in section 8) that for compactification on singular 7-folds to be possible, we need to consider not the 11D supergravity (SUGRA) approximation to M-theory but "full M-theory". Such singular compactifications are desirable due to the absence of chiral matter in smooth 7-fold compactifications.

In contrast, many publications on M-theory compactified on 7-folds seem to just do Kaluza-Klein reduction of 11D SUGRA on the singular 7-folds, not considering "full M-theory" (as far as I am concerned, the M2- and M5-branes are part of 11D SUGRA as solitonic objects, maybe I'm wrong/non-standard with that view?). One example of this is "On gauge enhancemenet and singular limits in $G_2$ compactifications of M-theory" by Halverson and Morrison, where no "full" M-theory is in sight as far as I can see. There are many other such papers where the SUGRA approximation is the essential starting point for the Kaluza-Klein reductions.

So what, exactly, is meant by Duff's remark that singular compactifications are only possible for "full M-theory"? In what way does this compactification of "full M-theory" differ from a standard Kaluza-Klein reduction, and how does it allow for singular compactifications while 11D SUGRA only allows for smooth compactifications?

  • $\begingroup$ I guess you have to read the following review. iopscience.iop.org/article/10.1088/0264-9381/19/22/301/meta. It is mentioned that supergravity approximation is not valid near singularities for some reason because otherwise it would not yield chiral fermions. $\endgroup$ – ved Dec 5 '16 at 9:00
  • $\begingroup$ @ved Hm, the only thing I can see there would be indeed the wrapping of the M2-brane which would be "M-theory", but as I already said in the question, this brane also occurs as a solitonic object in the SUGRA theory, so I'm still confused what "full M-theory" means here. $\endgroup$ – ACuriousMind Dec 5 '16 at 17:53
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    $\begingroup$ There is an answer at physicsoverflow.org/37968 $\endgroup$ – Arnold Neumaier Dec 12 '16 at 11:30

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