Virasoro constraints for topological recursion

2025/07/27 by Shuai Guo, Guo, Shuai, Qingsheng Zhang +1
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2507.20151

Abstract

This is the second paper in a series on \it Virasoro constraints for Cohomological Field Theory. We derive the ancestor Virasoro constraints for the topological recursion (TR) for an arbitrary spectral curve and establish the descendent Virasoro constraints for spectral curves satisfying certain conditions. For higher-genus curves, we further establish the corresponding ancestor and descendent Virasoro constraints for the associated non-perturbative generating series. We present several examples that illustrate the comparison between the descendent Virasoro constraints for TR descendent invariants and the original Virasoro constraints for geometric descendent invariants.

Citations

• Blobbed topological recursion and KP integrability
• Cohomological Field Theory with vacuum and its Virasoro constraints
• A generalization of the Witten conjecture through spectral curve
• BCOV's Feynman rule of quintic 3-folds
• Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves
• A matrix model for simple Hurwitz numbers, and topological recursion
• A holomorphic and background independent partition function for matrix models and topological strings
• Invariants of algebraic curves and topological expansion
• Gromov - Witten invariants and quantization of quadratic hamiltonians
• Semisimple Frobenius structures at higher genus

Related

• Virasoro Constraints of Curves as Residues
• Virasoro constraints for target curves
• Cohomological Field Theory with vacuum and its Virasoro constraints
• On the Virasoro Constraints for the Product Space X × C
• Virasoro constraints for stable pairs on toric 3-folds