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

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].