Non-compact Mirror Bundles and (0,2) Liouville Theories

TL;DR

This paper explores (0,2) deformations of Liouville theory and its mirror duality, using gauged linear sigma models to connect these deformations with gauge bundle moduli in non-compact Calabi-Yau manifolds.

Contribution

It introduces a gauged linear sigma model framework for (0,2) deformations of Liouville theory and establishes a mirror duality consistent with exact CFT results.

Findings

Gauged linear sigma model construction aligns with exact CFT analysis.

Deformation corresponds to non-trivial gauge bundles in heterotic compactifications.

Provides a new approach to study gauge bundle moduli in non-compact Calabi-Yau manifolds.

Abstract

We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the gauged linear sigma model completely agrees with the exact CFT analysis. In the context of heterotic string compactifications, the deformation corresponds to the introduction of a non-trivial gauge bundle. This non-compact Landau-Ginzburg construction yields a novel way to study the gauge bundle moduli for non-compact Calabi-Yau manifolds.