Orbifolds by cyclic permutations in gepner type superstrings and in the corresponding Calabi-Yau manifolds

Abstract

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 Z n 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 1 A , 16 3 E theory with respect to a phase Z 3 and a permutational Z 3 .