The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge ${\widehat{c}}_j(\sigma )=26f_j(\sigma )$, where $f_j(\sigma )$ is the length of cycle $j$ in twisted sector $\sigma$. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge $c_j(\sigma )=26$. These tools are used to begin the study of the target space-time dimension ${\widehat{D}}_j(\sigma )$ of cycle $j$ in sector $\sigma$, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the “pure” permutation orbifolds.