Mirror symmetry and new approach to constructing orbifolds of Gepner models

TL;DR

This work develops a locality- and space-time SUSY–driven framework for constructing orbifolds of Gepner models by leveraging spectral-flow generators to generate a complete physical state set. The core idea is to organize twisted sectors with an admissible group $G_{adm}$ and to select mutually local states using the mirror group $G^{*}_{adm}$, ensuring a modular-invariant spectrum. The construction yields massless NS and RR vertices, extends to all four vertex sectors via SUSY, and imposes GSO-type constraints that guarantee BRST invariance; modular invariance follows from the mutual locality relations linking $G_{adm}$ and $G^{*}_{adm}$. Significantly, the resulting physical state space coincides with previous Gepner-model results, while offering a transparent mirror-symmetric viewpoint and a robust method to generate consistent orbifolds with modular invariance.

Abstract

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from requirements of space-time supersymmetry and mutual locality, we construct a complete set of physical fields of orbifolds of Gepner models. To technically implement this, we use spectral flow generators to construct all physical fields from the chiral primary fields. The set of these spectral flow operators forms a so-called admissible group $G_{adm}$, which defines a given orbifold. The action of these operators produces a collection of physical fields consistent with the action of supersymmetry generators. The selection of mutually local fields from this collection is carried out using the mirror group $G^*_{adm}$. The permutation of $G_{adm}$ and $G^*_{adm}$ replaces the original orbifold with a mirror one that satisfies the same conditions as the original one. This also implies that the resulting model is modular invariant.