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


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Kondo S., Watari T.

COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol.367, no.1, pp.89-126, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 367 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1007/s00220-019-03302-0
  • Title of Journal : COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Page Numbers: pp.89-126

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.