Virasoro constraints for topological recursion

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.

28 pages