String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
COMMUNICATIONS IN MATHEMATICAL PHYSICS, cilt.367, sa.1, ss.89-126, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 367 Sayı: 1
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s00220-019-03302-0
- Dergi Adı: COMMUNICATIONS IN MATHEMATICAL PHYSICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.89-126
- Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Evet
Özet
It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Boltzmann-weighted (qL0-c/24-weighted) sum of U(1) charges with FeiF insertion computed in the Ramond sector.