As Mitchell points out, on page $91$ of the Witten and Gaiotto paper we see a pair of M5 branes. Recall that such a tetractys stands for the commutative form of length three qutrit paths, and is thus associated to the $3 \times 3$ $27$ dimensional Jordan algebra over the octonions. A necessary complexification leads to the $54$ dimensional bioctonion algebra.
There are no $11$ dimensional spacetimes in sight when discussing qutrits: just a few categorical diagrams and some very nice algebra. Why make M Theory harder than it needs to be?
6 years ago