Spin(11,1) String Theory

Spin(10), the covering group of SO(10), is a well-known promising grand unified group. Remarkably, Spin(10) chirality coincides with Dirac chirality, pointing to a nontrivial unification of Spin(10) and spacetime groups in Spin(11,1) that does not violate the Coleman-Mandula no-go theorem. The 11+1 dimensions of Spin(11,1) do not separate into a direct product of internal and spacetime dimensions. Rather, the 12 dimensions separate into a fermionic 10 dimensional internal compact manifold embedded inside 3+1 large spacetime dimensions. The 10 compact dimensions separate into a 4 dimensional weak manifold and a 6 dimensional color manifold that transform differently under Lorentz transformations. After symmetry breaking to the standard model, the weak and color manifolds together form a 10 dimensional Calabi-Yau manifold. The proposed Spin(11,1) string theory is a 26 dimensional tachyonic, nonsupersymmetric, anomaly-free bosonic string theory compactified to 12 dimensions on the maximal torus of the group SU(8)×SU(8). Weak and color gauge fields are carried by open bosonic strings whose ends attach to the fermionic weak and color subbranes of the Calabi-Yau manifold. Being nonsupersymmetric, the theory does not predict unobserved super-partners.