Counting BPS States via Holomorphic Anomaly Equations

  title={Counting BPS States via Holomorphic Anomaly Equations},
  author={Shinobu Hosono},
  journal={arXiv: High Energy Physics - Theory},
  • S. Hosono
  • Published 2002
  • Physics, Mathematics
  • arXiv: High Energy Physics - Theory
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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