Clifford(11,1) String Theory I: Geometry

This paper explores tachyonic, open bosonic string theory in which fermions are not strings, but rather reside on the D-brane boundary of open strings. The open-string tachyon is identified with a Higgs field transforming in the adjoint representation. The fermions of a generation of the standard model, including both internal and Weyl degrees of freedom, occupy a spinor representation of Spin(11,1) Spin ( 11 , 1 ) , and the Brauer-Weyl algebra of tensor products of the spinors is the Clifford algebra Cl(11,1) Cl ( 11 , 1 ) in 11+1 dimensions. The Chan-Paton condition that open strings transform in a tensor representation of the fermions at its endpoints requires the gauge group to be the group G²(10) = U(16) G 2 ( 10 ) = U ( 16 ) generated by multivectors of grade 2 (mod 4) of the transverse Clifford algebra Cl(10) Cl ( 10 ) . The U(1) U ( 1 ) factor of U(16) U ( 16 ) generates a transverse spatial rotation of the 3+1 large spacetime dimensions, leaving as internal gauge group the rank 15 subgroup SU(16) SU ( 16 ) . The 11+1 dimensions of the fermionic D-brane and the 15 dimensions of the bosonic torus combine to a total of 12+15 = 27 12 + 15 = 27 dimensions, one more than the 26 dimensions required by bosonic string theory. Grand symmetry breaking breaks SU(16) SU ( 16 ) to the rank 14 group SU(8)R × SU(8)L SU ( 8 ) R × SU ( 8 ) L , yielding a spacetime of 12+14 = 26 12 + 14 = 26 dimensions, as required by bosonic string theory.