Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We consider the generating function (prepotential) for Gromov-Witten invariants of rational elliptic surface. We apply the local mirror principle to calculate the prepotential and prove a certain recursion relation, holomorphic anomaly equation, for genus 0 and 1. We propose the holomorphic anomaly equation for all genera and apply it to determine higher genus Gromov-Witten invariants and also the BPS states on the surface. Generalizing Göttsche's formula for the Hilbert scheme of $g$ points on a surface, we find precise agreement of our results with the proposal recently made by Gopakumar and Vafa(hep-th/9812127).
27 pages, uses harvmac.tex; published form with note added in proof
27 pages, uses harvmac.tex; published form with note added in proof