Connecting the Kontsevich-Witten and Hodge tau-functions by the $\hat{GL(\infty)}$ operators

TL;DR

This paper provides an explicit formula linking the Kontsevich-Witten and Hodge tau-functions using $ abla$ operators, confirming a conjecture and advancing understanding of their relationship in mathematical physics.

Contribution

The paper introduces a new explicit formula connecting two important tau-functions via $ abla$ operators, confirming a conjecture by Alexandrov.

Findings

Established a formula connecting the tau-functions

Confirmed a conjecture by Alexandrov

Used Virasoro operators for the connection

Abstract

In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be connected using Virasoro operators. This proves a conjecture posted by Alexandrov in [1].