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(not an edit but to create the forum thread) Is the characterization in As an 11-dimensional boundary condition for the M2-brane complete or does one need to further extend by the m5 cocycle?
No, the point of what D’Auria & Fré introduced as the “hidden supergroup of 11d supergravity is that it is an ordinary super Lie 1-algebra, which in a sense serves as the 1-algebraic stand-in for the supergravity Lie 3-algebra.
See below the first diagram on p. 17 of Super-exceptional embedding construction of the M5-brane.
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pointer to
updated description of
(finally got a chance to go over the paper)
I don’t follow the logic of that article.
The first main claim wants to appear on the bottom of p. 2 “Therefore one obtains $D=10+1$ M-theory as a worldvolume theory […]”.
What actually happened before this “therefore” was the claim that a $D = 26+1$ extended susy algebra is a KK-reduction of one in $D=26+2$.
Nothing in this statement justifies or even makes plausible the conclusion that “Therefore one obtains $D=10+1$ M-theory as a worldvolume theory”.
The 10-brane term is already there in the $D=26+1$ algebra. The author would need to advance an argument that the worldvolume theory of that 10-brane is 11d Sugra.
Instead, he observes that a 10-brane term is also present in $D=26+2$. Even if true, this seems to be unrelated to the intended conclusion.
Unless and until this preprint gets updated with clarifications, I think it would be worthwhile to not have this recorded on the nLab.
You’re right, the indices around Eq6 still run all the way to 26, they don’t stop at 10. Just removed from the nLab page.
Right. Thanks.
Just to close this topic, I’ve contacted the author and indeed the step that would close the argument (that the 10-brane’s worldvolume theory is 11d M-theory) fully depends on the observations featured in Alessio et al.’s work. He then imagines that something similar is true in every dimension, but there is no evidence for this. The preprint only shows the very first necessary condition for something like this, that the branes that one would want to exhibit M theory as their worldvolume theory are present in higher-dimensional M theory.
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