Work

Virasoro constraints in quantum singularity theories

Year: 2025

Type: article

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.

Source: Journal of Geometry and Physics

DOI: 10.1016/j.geomphys.2025.105707

Authors: Weiqiang He, Yefeng Shen

Institutions: Sun Yat-sen University, University of Oregon

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Simons Foundation, Zhejiang University