The Monomial-Divisor Mirror Map for Landau-Ginzburg Orbifolds

TL;DR

This paper establishes a detailed geometric correspondence in Landau-Ginzburg orbifolds using toric geometry, leading to a monomial-divisor mirror map and discussing potential extensions to other models.

Contribution

It introduces an explicit geometric framework for Landau-Ginzburg orbifolds and derives the monomial-divisor mirror map using toric geometry techniques.

Findings

Established a one-to-one correspondence between certain states and blow-up forms.

Derived the monomial-divisor mirror map for Landau-Ginzburg orbifolds.

Discussed potential applications to other model types.

Abstract

We present the new explicit geometrical knowledge of the Landau-Ginzburg orbifolds, when a typical type of superpotential is considered. Relying on toric geometry, we show the one-to-one correspondence between some of the $(a,c)$ states with $U(1)$ charges $(-1,1)$ and the $(1,1)$ forms coming from blowing-up processes. Consequently, we find the monomial-divisor mirror map for Landau-Ginzburg orbifolds. The possibility of the application of the models of other types is briefly discussed.