2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152738We 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.9 pages, Latex 2.09, no figureHigh Energy Physics - TheoryAlgebraic Geometrytext