A Note On ADE String Compactifications

TL;DR

This paper investigates the use of m-invariants in N=2 super Virasoro algebra for constructing four-dimensional string models, identifying which invariants lead to consistent, supersymmetric spectra and exploring their mirror symmetry properties.

Contribution

It provides a classification of consistent string spectra derived from N=2 super Virasoro algebra invariants, highlighting the role of mirror symmetry and identifying pathological cases.

Findings

Out of the invariants studied, 529 yield consistent spectra.

210 spectra are mirrors of Gepner models.

76 spectra are real orbifolds with exact mirror symmetry.

Abstract

We address the question whether so-called m-invariants of the N=2 super Virasoro algebra can be used for the construction of reasonable four-dimensional string models. It turns out that an infinite subset of those are pathological in the sense that - although N=2 supersymmetric - the Ramond sector is not isomorphic to the Neveu-Schwarz sector. Consequently, these two properties are independent and only requiring both guarantees an N=1 space-time supersymmetric string spectrum. However, the remaining 529 consistent spectra - 210 of them are mirrors of Gepner models and 76 real orbifolds - show exact mirror symmetry and are contained in a recent classification of orbifolds of Gepner models.