Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture

Abstract

We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous Witten conjecture / Kontsevich theorem, where the link between the intersection theory of the moduli spaces and integrable systems is established via the geometry of double ramification cycles.

11 pages, some changes in the introduction

References in corpus (4)

• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• Vertices from replica in a random matrix theory
• Intersection numbers of Riemann surfaces from Gaussian matrix models

Cited by in corpus (1)

• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm