Extra Dimensions in Superstring Theory

Abstract

It was earlier shown that an SO(9,1) $θ^\a$ spinor variable can be constructed from RNS matter and ghost fields. $θ^\a$ has a bosonic worldsheet super-partner $λ^\a$ which plays the role of a twistor variable, satisfying $λΓ^μλ= \partial x^μ+iθΓ^μ\partialθ$. For Type IIA superstrings, the left-moving $[θ_L^\a,λ_L^\a]$ and right-moving $[θ_{R\a},λ_{R\a}]$ can be combined into 32-component SO(10,1) spinors $[θ^A,λ^A]$. This suggests that $λ^A Γ^{11}_{AB}λ^B= 2λ_L^\a λ_{R\a}$ can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA superstring and from consideration of $D_0$-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA superstring and an SO(9,1) x SO(2,1) structure for the Type IIB superstring.