Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface

Details Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface

1999-01-28

arxiv.org/abs/hep-th/9901151v4

Adv.Theor.Math.Phys.3:177-208,1999

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, uses harvmac.tex; published form with note added in proof

Scientific paper

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 G\"ottsche'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).

Affiliated with

Also associated with

No associations

Rating

Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-599205