Counting BPS States via Holomorphic Anomaly Equations

Abstract

We study Gromov-Witten invariants of a rational elliptic surface using holomorphic anomaly equation in [HST1](hep-th/9901151). Formulating invariance under the affine $E_8$ Weyl group symmetry, we determine conjectured invariants, the number of BPS states, from Gromov-Witten invariants. We also connect our holomorphic anomaly equation to that found by Bershadsky,Cecotti,Ooguri and Vafa [BCOV1](hep-th/9302103).

AMS-Latex, 30 pages; Table 3,4 and typos corrected and references added

References in corpus (6)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Disk Instantons, Mirror Symmetry and the Duality Web
• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
• Relative Lefschetz Action and BPS State Counting
• On N=1 Mirror Symmetry for Open Type II Strings
• Euler characteristics of SU(2) instanton moduli spaces on rational elliptic surfaces

Cited by in corpus (4)

• Direct Integration of the Topological String
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Topological Strings on Elliptic Fibrations