From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

Details From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

2011-11-22

arxiv.org/abs/1111.5349v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

In this letter we present our conjecture on the connection between the Kontsevich-Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. The important feature of this group element is its simplicity: 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.

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