Mottle calls it a twistor minirevolution. To stringers, this is the idea that one can completely reformulate the Standard Model without in any way affecting the physical basis for ordinary string theory. (I have personally heard some twistor mathematicians laugh at such nonsense, but what would they know?) Anyway, it seems that most stringers are rather unkeen to investigate ternary extensions of basic twistor geometry.
Thanks to kneemo's excellent advice I have lately been reading two wonderful papers (by Corinne Manogue and collaborators) on an octonion analogue of the complex group with which one begins to study twistors, namely $SL(2,C)$. The 2009 paper defines a group $SL(3,O)$ over the octonions. This behaves like the group $E_6$, which contains many subgroups of interest to stringers, such as three copies of $SO(9,1)$, acting on a $10$ dimensional Lorentzian space. This group is like the octonion group $SL(2,O)$, built from complex octonion matrices. We could also make $3 \times 3$ matrices with $2 \times 2$ blocks from $SL(2,O)$.
7 years ago