GLSM realizations of maps and intersections of Grassmannians and Pfaffians

TL;DR

This paper constructs gauged linear sigma models (GLSMs) for various complex geometries, including intersections of Grassmannians, Pfaffians, and Calabi-Yau manifolds, expanding the toolkit for string compactifications and geometric realizations.

Contribution

It introduces new GLSM realizations for maps like Veronese and Segre embeddings, and for intersections of Grassmannians and Pfaffians, including exotic Calabi-Yau constructions, with detailed duality analyses.

Findings

GLSMs for intersections of Grassmannians and Pfaffians are explicitly constructed.

Dualities in nonabelian gauge factors reveal different geometric phases.

Perturbative and quantum effects realize different geometric phases in the models.

Abstract

In this paper we give gauged linear sigma model (GLSM) realizations of a number of geometries not previously presented in GLSMs. We begin by describing GLSM realizations of maps including Veronese and Segre embeddings, which can be applied to give GLSMs explicitly describing constructions such as the intersection of one hypersurface with the image under some map of another. We also discuss GLSMs for intersections of Grassmannians and Pfaffians with one another, and with their images under various maps, which sometimes form exotic constructions of Calabi-Yaus, as well as GLSMs for other exotic Calabi-Yau constructions of Kanazawa. Much of this paper focuses on a specific set of examples of GLSMs for intersections of Grassmannians G(2,N) with themselves after a linear rotation, including the Calabi-Yau case N=5. One phase of the GLSM realizes an intersection of two Grassmannians, the other phase realizes an intersection of two Pfaffians. The GLSM has two nonabelian factors in its gauge group, and we consider dualities in those factors. In both the original GLSM and a double-dual, one geometric phase is realized perturbatively (as the critical locus of a superpotential), and the other via quantum effects. Dualizing on a single gauge group factor yields a model in which each geometry is realized through a simultaneous combination of perturbative and quantum effects.