2013/12/27 by Siqi Liu, Liu, Si-Qi, Yongbin Ruan +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1312.7227
openalex publication_date 2013/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
According to the ADE Witten conjecture, which is proved by Fan, Jarvis and Ruan, the total descendant potential of the FJRW invariants of an ADE singularity is a tau function of the corresponding mirror ADE Drinfeld-Sokolov hierarchy. In the present paper, we show that there is a finite group Γ acting on a certain ADE singularity which induces an action on the corresponding FJRW-theory, and the Γ-invariant sector also satisfies the axioms of a cohomological field theory except the gluing loop axiom. On the other hand, we show that there is also a Γ-action on the mirror Drinfeld-Sokolov hierarchy, and the Γ-invariant flows yield the BCFG Drinfeld-Sokolov hierarchy. We prove that the total descendant potential of the Γ-invariant sector of a FJRW-theory is a tau function of the corresponding BCFG Drinfeld-Sokolov hierarchy.