• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,728 comments
1,470 users with positive rep
818 active unimported users
More ...

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

+ 7 like - 0 dislike

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

asked Dec 2, 2016 in Theoretical Physics by ACuriousMind (910 points) [ revision history ]
edited Dec 11, 2016 by Dilaton
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

1 Answer

+ 3 like - 0 dislike

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 40227 (5,140 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights