# 11d SuGra from the torsion constraint

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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

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