String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication

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Kondo S., Watari T.

COMMUNICATIONS IN MATHEMATICAL PHYSICS, cilt.367, sa.1, ss.89-126, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 367 Konu: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00220-019-03302-0
  • Sayfa Sayıları: ss.89-126


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.