# Mirror Symmetry for Nonabelian Landau-Ginzburg Models

## TL;DR

This paper develops a mirror symmetry framework for nonabelian Landau-Ginzburg models, introducing a dual group and explicit mirror maps, expanding the understanding of mirror symmetry beyond abelian cases.

## Contribution

It introduces a non-abelian dual group and constructs explicit mirror maps for nonabelian LG models, demonstrating their isomorphism in specific sectors.

## Key findings

- Defined the non-abelian dual group G* for mirror LG models
- Constructed explicit mirror maps between A-model and B-model
- Proved isomorphism of mirror maps in specific sectors for Fermat polynomials

## Abstract

We consider Landau-Ginzburg models stemming from groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group $G^\star$, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials., we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials.