A simple proof of Witten conjecture through localization

TL;DR

This paper presents a straightforward proof of Witten's conjecture by deriving relations between linear Hodge integrals and demonstrating that the initial non-trivial relation suffices to establish the theorem.

Contribution

The paper introduces a simple proof of Witten's conjecture using relations between Hodge integrals, simplifying previous approaches.

Findings

Derived a system of relations between linear Hodge integrals.

Showed that the first non-trivial relation implies Witten's conjecture.

Provided a more straightforward proof of the Kontsevich Theorem.

Abstract

We obtain a system of relations between linear Hodge integrals. As an application, we show that its first non-trivial relation implies the Witten's Conjecture/Kontsevich Theorem.