ADE string vacua with discrete torsion

TL;DR

This paper classifies (2,2) string vacua constructed from ADE minimal models using Landau-Ginzburg techniques, identifying all spectra and discovering new mirror pairs missed by previous methods.

Contribution

It provides a complete classification of (2,2) vacua with ADE invariants, systematically avoiding redundancies and uncovering new mirror pairs.

Findings

Recovered known (2,2) vacua spectra

Discovered 4 new mirror pairs

Identified relations between redundant spectra and certain groups

Abstract

We complete the classification of (2,2) string vacua that can be constructed by diagonal twists of tensor products of minimal models with ADE invariants. Using the \LG\ framework, we compute all spectra from inequivalent models of this type. The completeness of our results is only possible by systematically avoiding the huge redundancies coming from permutation symmetries of tensor products. We recover the results for (2,2) vacua of an extensive computation of simple current invariants by Schellekens and Yankielowitz, and find 4 additional mirror pairs of spectra that were missed by their stochastic method. For the model $(1)^9$ we observe a relation between redundant spectra and groups that are related in a particular way.