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

TL;DR

This paper advances the understanding of orbifold-string theories by analyzing cycle dynamics and target space-time dimensions, providing new formulations of physical-state conditions and initial results for permutation orbifolds.

Contribution

It introduces extended Virasoro generators with cycle-dependent central charge and a reduced formulation, enabling the study of target space-time dimensions in permutation orbifold sectors.

Findings

Derived cycle-dependent Virasoro generators with extended central charge

Formulated reduced physical-state conditions at standard central charge

Initiated analysis of target space-time dimensions based on zero modes

Abstract

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 $\hat{c}_j(\sigma)=26f_j(\sigma)$, 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 $\hat{D}_j(\sigma)$ 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.