Higher-genus wall-crossing in Landau-Ginzburg theory

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.

Two errors are fixed. The theorems listed in the introduction are not changed. 1. In Lemma 16, there should not be a truncation for the series mu. 2. The formula for mu in Remark 8 is corrected