# Why is full M-theory needed for compactification on singular 7-folds and what does that even mean?

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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?

This post imported from StackExchange Physics at 2016-12-11 20:43 (UTC), posted by SE-user ACuriousMind

edited Dec 11, 2016
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.

This post imported from StackExchange Physics at 2016-12-11 20:43 (UTC), posted by SE-user ved
@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.

This post imported from StackExchange Physics at 2016-12-11 20:43 (UTC), posted by SE-user ACuriousMind

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The description of M2 and M5-branes as solitonic objects in the 11D SUGRA is only valid when their mass is much bigger than the Planck mass. When their mass goes to zero, as it is the case if they are wrapped around cycles shrinking to zero size to form a singularity, the SUGRA approxiation breaks down and it is a non-trivial claim about M-theory that they give rise to new massless degrees of freedom, which are not present in the ordinary massless (Kaluza-Klein reduced) spectrum of 11d SUGRA.

Equivalently, it is not clear how a classical field theory as 11d SUGRA makes sense on a singular space, whereas M-theory does because the shrinking M-branes keep the physics smooth.

answered Dec 11, 2016 by (4,800 points)

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