Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties

TL;DR

This paper introduces two nonabelian gauge theory models, PAX and PAXY, that describe string propagation on determinantal Calabi-Yau varieties, expanding the understanding of string compactifications beyond complete intersections.

Contribution

It develops and analyzes two novel nonabelian GLSM constructions, PAX and PAXY, for determinantal Calabi-Yau varieties, establishing their duality and exploring their quantum Kähler moduli space.

Findings

PAX and PAXY models are dual descriptions of the same physics.

The quantum Kähler moduli space matches existing literature.

The models extend the class of Calabi-Yau geometries studied in string theory.

Abstract

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum K\"ahler moduli space of these varieties and find no disagreement with existing results in the literature.