String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol.367, no.1, pp.89-126, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 367 Issue: 1
- Publication Date: 2019
- Doi Number: 10.1007/s00220-019-03302-0
- Journal Name: COMMUNICATIONS IN MATHEMATICAL PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.89-126
- Middle East Technical University Northern Cyprus Campus Affiliated: Yes
Abstract
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.