Shifted Z 6 Orbifold Model and 1 · 4 Model Hiroshi

A huge number of four-dimensional string vacua are derived from several types of constructions, e.g., orbifold models,l) tensoring of coset constructions) and so on. It is very important to relate models obtained by different constructions ) and further . to understand the whole vacua in a unified framework. For example, some Gepner's models have the same generation numbers as orbifold models.) It is meaningful to investigate in more detail the relations of the models besides coincidence of the massless spectra. In the Esx E8 heterotic string theory, internal spaces of the four-dimensional string vacua are represented in terms of the N =2 superconformal field theories (SCFTs) with c=9, as well as the 50(10) x E8 internal space for the left-mover. The huge number of string vacua implies that there are lots of possibilities to construct c=9 SCFTs. For example, c=9 theories in the orbifold models are represented in terms of six-dimensional superstring satisfying twisted boundary conditions, where we call the superstring super-orbifold models. In the Gepner's models, c=9 theories are constructed by tensoring of N =2 minimal models. Recently, it has been shown that two-dimensional Z3,Z4 and Z6 super-orbifold models are equivalent to 1, 22 and 1·4 theories, respectively, from the point of view of the SCFT.)-7) Those are applied to correspondence between 1 (2) models and Z3 x Z3 (Z4 x Z4) orbifold models at the maximal enhancement point in the (2, 2) heterotic construction. In Ref. 7), it has been verified that the two-dimensional twisted superorbifold models are equivalent to c = 3 tensoring of the minimal models. On the other hand, the shifted orbifolds**) equivalent to the twisted orbifolds were treated in Ref. 5) (6)), where it has been clarified that the two-dimensional shifted Z3 (Z4) superorbifold model is one sort of free-bosonic representations of the 1 (22) SCFT. The shifted formalism represents an enhanced U(l) diagonal basis naturally. In addition, *) Fellow of the Japan Society for the Promotion of Science. **) Some of them are represented by covariant self-dual lattices in Ref. 8).