Non-Perturbative Superpotentials in Landau-Ginzburg Compactification

TL;DR

This paper investigates Landau-Ginzburg models related to Calabi-Yau four-folds, constructing indices for toric divisors to determine their potential to generate non-perturbative superpotentials, and explores phase transitions via orbifold constructions.

Contribution

It introduces a method to identify when divisors can generate superpotentials after orbifoldization, extending understanding of non-perturbative effects in Landau-Ginzburg models.

Findings

Constructed indices for toric divisors in Landau-Ginzburg models.

Identified conditions under which divisors generate superpotentials.

Provided a method to induce superpotential generation through orbifoldization.

Abstract

We study the Landau-Ginzburg models which correspond to Calabi-Yau four-folds. We construct the index of the typical states which correspond to toric divisors. This index shows that whether a corresponding divisor can generate a non-perturbative superpotential. For an application, we consider the phase transition in terms of the orbifold construction. We obtain the simple method by which the divisor, which can not generate a superpotential in the original theory, can generate a superpotential after orbifoldization.