THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE III: LORENTZIAN AND EUCLIDEAN SPACE—TIMES IN A LARGE EXAMPLE

Abstract

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the target space–time dimension[Formula: see text], the target space–time signature and the target space–time symmetry of each cycle j in each twisted sector σ. We find in particular a gratifying space–time symmetry enhancement which naturally matches the space–time symmetry of each cycle to its space–time dimension. Although the orbifolds of ℤ2-permutation-type are naturally Lorentzian, we find that the target space–times associated with larger permutation groups can be Lorentzian, Euclidean and even null [Formula: see text], with varying space–time dimensions, signature and symmetry in a single orbifold.