| 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 \({\widehat{GL(\infty)}}\) group. Indeed, we show that the two tau-functions can be connected using Virasoro operators. This proves a conjecture posted by Alexandrov in (From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators, Letters in Mathematical physics, doi:10.1007/s11005-013-0655-0, 2014). |
