Holomorphic anomalies in topological field theories

Creators: Bershadsky, M.; Cecotti, S.; Ooguri, H.; Vafa, C.

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Abstract

We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.

Additional Information

© 1993 Elsevier. Received 5 March 1993, Accepted 26 April 1993. We would like to thank I. Antoniadis, L. Dixon and S.T. Yau for valuable discussions. We would also like to thank S. Hosono for sharing his Mathematica program for the examples we used in this paper. We are also grateful to S. Katz for explaining the origin of the genus zero contribution (see appendix B) that we had discovered experimentally. The research of M. B., H. O. and C. V. was supported in part by Packard fellowship and NSF grants PHY-87-14654 and PHY-89-57162. The research of S. C. was supported in part by INFN. The research of H. O. was also supported in part by Grant-in-Aid for Scientific Research on Priority Areas 231 'Infinite Analysis' from the Ministry of Education, Science and Culture of Japan.

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