Virasoro constraints and Hurwitz numbers through asymptotic analysis

Yon-Seo Kim and Kefeng Liu

Vol. 241 (2009), No. 2, 275–284

DOI: 10.2140/pjm.2009.241.275

Abstract

We present a new method, using asymptotic analysis, to obtain a system of recursion relations for integrals on moduli spaces of curves. By applying the asymptotic analysis on the join-cut relation of the ELSV formula, we derive the recursion relation of R. Dijkgraaf and E. and H. Verlinde, which is exactly the Virasoro constraints for topological gravity. This gives an alternative proof of Witten’s Conjecture using asymptotic analysis.

Keywords

Hurwitz, Gromov, Witten, asymptotic, ELSV, Stirling, Witten conjecture, Kontsevich

Mathematical Subject Classification 2000

Primary: 51P05

Secondary: 81R10

Milestones

Received: 24 April 2008

Revised: 27 January 2009

Accepted: 29 January 2009

Published: 1 June 2009