GLSMs, joins, and nonperturbatively-realized geometries

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.