Clifford(11,1) String Theory II: Strings

Abstract This paper continues the exploration of a tachyonic, bosonic string theory in which fermions are not strings, but rather occupy a curved D-brane boundary of open strings, and the open-string tachyon supplies the Higgs sector. The fermionic D-brane occupies the 11 + 1 dimensions of the Clifford algebra $$\text {Cl}(11,1)$$ Cl ( 11 , 1 ) , while open strings fill out the additional 14 dimensions of a maximal torus of the rank 14 subgroup $$\text {SU}(8)_R \times \text {SU}(8)_L$$ SU ( 8 ) R × SU ( 8 ) L of the group $$G^2(10) = \text {U}(16)$$ G 2 ( 10 ) = U ( 16 ) generated by multivectors of grade 2 (mod 4) in $$\text {Cl}(10)$$ Cl ( 10 ) , for a total of $$12{+}14 = 26$$ 12 + 14 = 26 dimensions. An important result is that there exist open-string solutions whose D-brane boundary is curved, but those solutions are purely holomorphic (right-moving) or purely antiholomorphic (left-moving) without an associated closed string solution. The only closed-string modes are completely neutral under all internal gauge transformations; for massless modes, these comprise just 4 modes, the spin $$\pm 2$$ ± 2 graviton, and two spin 0 modes, the scalar dilaton and the pseudoscalar 2-form.