From Hurwitz to Kontsevich-Witten via Virasoro

摘要

In this letter we present our conjecture on the connection between the Kontsevich-Witten and Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the GL(∞) group element, and the important feature is that the corresponding operator is quite simple: it is built of only generators of the Virasoro algebra. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich-Witten tau-function.