Landau-Ginzburg String Vacua

TL;DR

This paper explores a large class of Landau-Ginzburg models with isolated singularities, analyzing their properties, symmetries, and connections to Calabi-Yau manifolds, revealing insights into their topological and mirror symmetry aspects.

Contribution

It characterizes over three thousand Landau-Ginzburg models with isolated singularities and clarifies their relation to Calabi-Yau manifolds, including cases beyond the standard framework.

Findings

Euler numbers range from -960 to 960.

The models exhibit high symmetry but lack complete mirror pairing.

Topological identities link these models to broader classes of Calabi-Yau manifolds.

Abstract

We investigate a class of (2,2) supersymmetric string vacua which may be represented as Landau--Ginzburg theories with a quasihomogeneous potential which has an isolated singularity at the origin. There are at least three thousand distinct models in this class. All vacua of this type lead to Euler numbers which lie in the range $-960 \leq \chi \leq 960$. The Euler characteristics do not pair up completely hence the space of Landau--Ginzburg ground states is not mirror symmetric even though it exhibits a high degree of symmetry. We discuss in some detail the relation between Landau--Ginzburg models and Calabi--Yau manifolds and describe a subtlety regarding Landau--Ginzburg potentials with an arbitrary number of fields. We also show that the use of topological identities makes it possible to relate Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual Landau-Ginzburg framework does not apply.