Clifford(11,1) String Theory

In 1935, Brauer and Weyl proved the theorem that the algebra of outer products of spinors (the spinor representation of the rotation group) is isomorphic to the Clifford algebra Cl(K,M) in an arbitrary number K+M of spacetime dimensions. The observed relation between fermions and bosons seen in the Standard Model of physics agrees with the Brauer-Weyl theorem, but not with supersymmetry. Astonishingly, none of the canonical string theory textbooks mentions the Brauer-Weyl theorem; indeed a search on the NASA-ADS, Inspire, and arXiv databases reveals zero citations of the theorem in any string-theory paper (although the theorem is well-known in the mathematical literature).

The Brauer-Weyl theorem is consistent with old-fashioned nonsupersymmetric open bosonic string theory in which fermions live on an 11+1 dimensional D-brane boundary of open bosonic strings, and bosons are compactified on a 14-dimensional maximal torus of SU(8)_R×SU(8)_L, filling out 26 dimensions in all. The textbook objections to bosonic string theory do not hold up under rigorous scrutiny.