A new method toward the Landau-Ginzburg/Calabi-Yau correspondence via quasi-maps

TL;DR

This paper introduces a novel approach using quasi-maps and stability conditions to connect Gromov-Witten invariants of Calabi-Yau 3-folds with Fan-Jarvis-Ruan-Witten invariants of Landau-Ginzburg models, advancing the Landau-Ginzburg/Calabi-Yau correspondence.

Contribution

It develops a new framework involving quasi-maps and stability conditions to interpolate between Gromov-Witten and FJRW invariants, providing a geometric bridge.

Findings

Establishes a sequence of stability conditions for quasi-maps.

Interpolates between Gromov-Witten and FJRW moduli stacks.

Provides new insights into the Landau-Ginzburg/Calabi-Yau correspondence.

Abstract

The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In this paper, we consider the stack of quasi-maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for Gromov-Witten invariants and the moduli stack for Fan-Jarvis-Ruan-Witten invariants.