Intersection numbers on Deligne-Mumford moduli spaces and quantum Airy curve

TL;DR

This paper proves a special case of a conjecture relating intersection numbers on moduli spaces of algebraic curves to the quantum Airy curve, using Virasoro constraints.

Contribution

It establishes the Airy curve case of Gukov and Sulkowski's conjecture by connecting intersection theory with Virasoro constraints.

Findings

Confirmed the conjecture for the Airy curve case.

Linked intersection numbers to quantum Airy curve via Virasoro constraints.

Provided a reduction to known Virasoro constraints for proof.

Abstract

We establish the Airy curve case of a conjecture of Gukov and Su{\l}kowski by reducing to Dijkgraaf-Verlinde-Verlinde Virasoro constraints satisfied by the intersection numbers on moduli spaces of algebraic curves.