Higher-genus wall-crossing in Landau-Ginzburg theory

TL;DR

This paper establishes a comprehensive wall-crossing formula for higher-genus Landau-Ginzburg theories associated with Fermat quasi-homogeneous polynomials, extending previous genus-specific results through localization techniques.

Contribution

It introduces a new localization-based proof of wall-crossing formulas in all genera for Landau-Ginzburg theories, generalizing earlier genus-zero and genus-one results.

Findings

Proves a universal wall-crossing formula for all genera.

Constructs a master space with an added tangent vector for localization.

Extends quasi-map wall-crossing results to Landau-Ginzburg setting.

Abstract

For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan-Jarvis-Ruan-Witten theory with narrow insertions. We prove a wall-crossing formula in all genera via localization on a master space, which is constructed by introducing an additional tangent vector to the moduli problem. This is a Landau-Ginzburg theory analogue of the higher-genus quasi-map wall-crossing formula proved by Ciocan-Fontanine and Kim. It generalizes the genus-$0$ result by Ross-Ruan and the genus-$1$ result by Guo-Ross.