No Mirror Symmetry in Landau-Ginzburg Spectra!

TL;DR

This paper classifies Landau-Ginzburg potentials for N=2 superconformal field theories with c=9, revealing that many models lack mirror symmetry, challenging previous assumptions about spectral symmetry in these theories.

Contribution

It provides a comprehensive classification of LG potentials using recent polynomial classifications and analyzes their mirror symmetry properties, uncovering unexpected asymmetries.

Findings

Most models lack mirror partners.

Models with known mirror constructions show strong symmetry.

Approximately 15% of models have no mirror symmetry.

Abstract

We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate the corresponding Hodge numbers. Surprisingly, the resulting spectra are less symmetric than the existing incomplete results. It turns out that models belonging to the large class for which an explicit construction of a mirror model as an orbifold is known show remarkable mirror symmetry. On the other hand, half of the remaining 15\% of all models have no mirror partners. This lack of mirror symmetry may point beyond the class of LG-orbifolds.