Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties

TL;DR

This paper explores gauged linear sigma models for noncompact Calabi-Yau manifolds, revealing multiple phases, effective theories, and dualities, including mirror symmetry and Liouville theories, advancing understanding of their geometric and conformal field theory aspects.

Contribution

It introduces a detailed analysis of phases and dualities in gauged linear sigma models for noncompact Calabi-Yau varieties, connecting them with Liouville and Landau-Ginzburg theories.

Findings

Four massless effective theories related by topology change and dualities.

Identification of mirror dual Calabi-Yau geometries in T-dual theories.

Effective theories realized as N=2 Liouville coupled with Landau-Ginzburg models.

Abstract

We study gauged linear sigma models for noncompact Calabi-Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet-Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. We find four massless effective theories in the infrared limit, which are related to each other under the Calabi-Yau/Landau-Ginzburg correspondence and the topology change. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: One is the sigma model on a newly obtained Calabi-Yau geometry as a mirror dual, while the other is given by a Landau-Ginzburg theory with a negative power term, indicating N=2 superconformal field theory on SL(2,R)/U(1). We argue that the effective theories in the original gauged linear sigma model are exactly realized as N=2 Liouville theories coupled to well-defined Landau-Ginzburg minimal models.