# Counting BPS States via Holomorphic Anomaly Equations

@article{Hosono2002CountingBS, title={Counting BPS States via Holomorphic Anomaly Equations}, author={Shinobu Hosono}, journal={arXiv: High Energy Physics - Theory}, year={2002} }

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).

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