Quantcast
  • 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.

News

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

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  11d SuGra from the torsion constraint

+ 3 like - 0 dislike
618 views

There is a most curious phenomenon in supergravity:

Generally, the equations of motion of supergravity theories are equivalent to the Bianchi identities combined with just a kind of super-holomophicity known as "superspace constraints" or "rheonomy" (D'Auria-Fre 80s). This is already remarkable in itself, but what is even more remarkable is that for 11-dimensional sugra (but, as far as I am aware, for no theory with lower dimension/lower supersymmetry) the constraints and hence the equations of motion are all equivalent to (Bianchi identities and) just one single torsion constraint: the torsion of the curved superspacetime in each tangent space has to be the canonical torsion of the M2-extended super Minkowski spacetime. This is due to Howe 97.

Has this result been followed up much? I am aware of CGNN 00 which tries to go off-shell with this. But to me it seems that the sheer nicety of the above result suggest rather different ways of bringing in higher order corrections.

I may be wrong about this, but what is true is that due to the above fact 11d SuGra has a strinkingly elegant mathematical formulation: it's precisely about the higher super Cartan geometry modeled on the M2-extended super Minkowski with its canonical torsion. This is mathematically such an elementary (in the sense of: fundamental) concept that it may be  axiomatized in just homotopy-type theory with six modalities added. (Or so I claim, am preparing some notes).

So it makes one wonder, doesn't it. This contrasts however with the scarcity of followups in the literature the I see. I there any substantial further development building on or inspired by Howe 97?

asked Jan 24, 2015 in Theoretical Physics by Urs Schreiber (6,095 points) [ revision history ]

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:
$\varnothing\hbar$ysicsOverflow
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
...