ORBIFOLDS BY CYCLIC PERMUTATIONS IN GEPNER TYPE SUPERSTRINGS AND IN THE CORRESPONDING CALABI-YAU MANIFOLDS

Left-right symmetric tensor products of minimal n = 2 superconformal theories allow for the construction of a consistent inner sector of the heterotic string. Such Gepner models often have a cyclic permutational symmetry of identical factor theories. We discuss the massless spectrum of orbifolds with respect to these symmetries and compare it to that of the corresponding resolved Calabi-Yau orbifolds, finding full agreement. We also discuss the orbifoldisation with respect to a combination of Zn phase symmetries and the cyclic permutational symmetries. The resulting quark-lepton generation numbers are in general divisible by 6 or 4. The only exception is still the well-known three generation model, an orbifold of the 1A, 163E theory with respect to a phase Z3 and a permutational Z3. © 1992 Academic Press, Inc. All rights reserved.