Counting BPS States via Holomorphic Anomaly Equations

Shinobu Hosono

paper

Counting BPS States via Holomorphic Anomaly Equations

arXiv:hep-th/0206206

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