Virasoro constraints for topological recursion

TL;DR

This paper extends Virasoro constraints to topological recursion for arbitrary spectral curves, establishing both ancestor and descendent constraints, and compares these with geometric invariants through multiple examples.

Contribution

It derives Virasoro constraints for topological recursion on arbitrary spectral curves and establishes their relation to geometric invariants, including higher-genus cases.

Findings

Derived ancestor Virasoro constraints for topological recursion.

Established descendent Virasoro constraints under specific conditions.

Compared descendent constraints with geometric invariants through examples.

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.