Virasoro constraints in quantum singularity theories
Abstract
We introduce Virasoro operators for any Landau-Ginzburg pair (W, G) where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We propose a conjecture that the total ancestor potential of the FJRW theory of the pair (W,G) is annihilated by these Virasoro operators. We prove the conjecture in various cases, including: (1) invertible polynomials with the maximal group, (2) some two-variable polynomials with the minimal group, (3) certain Calabi-Yau polynomials with groups. We also discuss the connections among Virasoro constraints, mirror symmetry of Landau-Ginzburg models, and Landau-Ginzburg/Calabi-Yau correspondence.
Cite
@article{arxiv.2103.00313,
title = {Virasoro constraints in quantum singularity theories},
author = {Weiqiang He and Yefeng Shen},
journal= {arXiv preprint arXiv:2103.00313},
year = {2022}
}
Comments
3nd version, 37 pages, Section 3.3 is revised, Appendix B is added. Comments welcome!