Communications in Mathematical Physics

, Volume 106, Issue 1, pp 1–40 | Cite as

Theta functions, modular invariance, and strings

  • Luis Alvarez-Gaumé
  • Gregory Moore
  • Cumrun Vafa


We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.


Neural Network Statistical Physic Complex System String Theory Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Luis Alvarez-Gaumé
    • 1
  • Gregory Moore
    • 1
  • Cumrun Vafa
    • 1
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA

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