Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds and global tt^* geometry

TL;DR

This paper explores the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit, establishing a global mirror symmetry framework with logarithmic poles and tt*-geometry for crepant resolutions.

Contribution

It introduces a global moduli space for toric orbifolds with crepant resolutions and demonstrates the existence of tt*-geometry in this global setting.

Findings

Mirror symmetry as an isomorphism of Frobenius manifolds with logarithmic poles

Construction of a global B-model moduli space for crepant resolutions

Existence of tt*-geometry globally on the moduli space

Abstract

We discuss the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit. This enables us to express mirror symmetry as an isomorphism of Frobenius manifolds which aquire logarithmic poles along a boundary divisor. If the toric orbifold admits a crepant resolution we construct a global moduli space on the B-side and show that the associated tt^*-geometry exists globally.