# GLSMs, joins, and nonperturbatively-realized geometries

## TL;DR

This paper constructs gauged linear sigma models (GLSMs) for pairs of dual Calabi-Yau manifolds, illustrating how joins and strong-coupling effects lead to nonperturbative geometric realizations.

## Contribution

It provides a GLSM framework for homologically projective dual Calabi-Yaus, incorporating joins and dualities to realize geometries through perturbative and non-perturbative effects.

## Key findings

- GLSM realizations of dual Calabi-Yaus via joins
- Dual GLSMs exhibit perturbative and non-perturbative phases
- Application of gauge dualities to construct dual models

## Abstract

In this work we give a gauged linear sigma model (GLSM) realization of pairs of homologically projective dual Calabi-Yaus that have recently been constructed in the mathematics literature. Many of the geometries can be realized mathematically in terms of joins. We discuss how joins can be described in terms of GLSMs and how the associated Calabi-Yaus arise as phases in the GLSMs. Due to strong-coupling phenomena in the GLSM, the geometries are realized via a mix of perturbative and non-perturbative effects. We apply two-dimensional gauge dualities to construct dual GLSMs. Geometries that are realized perturbatively in one GLSM, are realized non-perturbatively in the dual, and vice versa.