Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface

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dc.creatorHosono, S.
dc.creatorSaito, M. -H.
dc.creatorTakahashi, A.
dc.date1999-01-28
dc.date1999-12-29
dc.date.accessioned2026-07-07T11:36:19Z
dc.date.available2026-07-07T11:36:19Z
dc.descriptionWe 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).
dc.description27 pages, uses harvmac.tex; published form with note added in proof
dc.identifierhttps://arxiv.org/abs/hep-th/9901151
dc.identifierhttp://arxiv.org/abs/hep-th/9901151
dc.identifierAdv.Theor.Math.Phys.3:177-208,1999
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198880
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleHolomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface
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