Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models

TL;DR

This paper constructs and analyzes a class of two-dimensional supersymmetric gauged linear sigma models with various phases, revealing new equivalences in D-brane categories and surprising dualities between different Calabi-Yau manifolds.

Contribution

It systematically develops one-parameter models with unbroken gauge subgroups, extending known examples to include diverse Calabi-Yau and non-Calabi-Yau manifolds, and predicts novel dualities.

Findings

Identifies models with unbroken gauge subgroups in different phases.

Predicts equivalences of D-brane categories across models.

Discovers identical quantum Kähler moduli spaces for distinct Calabi-Yau threefolds.

Abstract

We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a recently developed technique. The focus of the present work is on models with one K\"ahler parameter. The models include those corresponding to Calabi-Yau threefolds, extending three examples found earlier by a few more, as well as Calabi-Yau manifolds of other dimensions and non-Calabi-Yau manifolds. The construction leads to predictions of equivalences of D-brane categories, systematically extending earlier examples. There is another type of surprise. Two distinct superconformal field theories corresponding to Calabi-Yau threefolds with different Hodge numbers, $h^{2,1}=23$ versus $h^{2,1}=59$, have exactly the same quantum K\"ahler moduli space. The strong-weak duality plays a crucial r\^ole in confirming this, and also is useful in the actual computation of the metric on the moduli space.