If the 1998 paper by Castellani et al. below is right,

http://arxiv.org/abs/hep-th/9803039

then all such solutions including Englert's elegant solution – cited as [13] above – are dual to $G/H$ M$p$-branes which are described as solutions interpolating between flat space at infinity and some $G/H$ configuration near the horizon. Let me admit that I don't quite understand the paper – it seems to imply the existence of lots of new objects in ordinary decompactified M-theory.

Of course, as discussed above, the lack of supersymmetry reduces the probability that it makes sense to try to locate the object in any dual description. The stability of such non-SUSY solutions is only restored in some "large radii" limit and is completely lost in the opposite limit. Still, there are some moral examples where it makes sense to trace unstable objects to a dual description although their masses and tensions of course fail to be calculable from SUSY which isn't there. Various authors such as Gauntlett et al.

http://arxiv.org/abs/hep-th/0505207

have mentioned Englert's solution but discarded it because of the instability. You may also want to look at the octonion membrane by Duff et al.:

http://arxiv.org/abs/hep-th/9706124

It's probably not quite equivalent to Englert's solution but seems to be an object of the same dimension with the same algebraic niceties hidden in the core.

Some possibly very similar candidate dual CFTs (also citing Englert) are constructed by Fabbri et al.:

http://arxiv.org/abs/hep-th/9907219

Also, Englert's solution might have a weak $G_2$ holonomy

http://www.sciencedirect.com/science/article/pii/S0550321302000421

although this statement of mine could be complete nonsense: I don't have the access to the full paper. In 2008, Klebanov et al. studied dual CFTs to squashed spheres

http://arxiv.org/abs/0809.3773

that are claimed to be of Englert's type.

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