Modular Invariance of Field Theories and String Compactifications

  • A. Shapere
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 47)


There is a large class of Gaussian lattice models which are self-dual with respect to inversion of coupling constants. When a theta term is added, this duality may extend to an invariance under an action of an infinite discrete modular group on the coupling parameter space. In particular, 4-dimensional Abelian lattice gauge theories possess a Sp(2k, Z) modular symmetry, and string compactifications on d-dimensional tori are invariant under SO(16 + d, d; Z). We review these results and their applications, and discuss the classification of self-dual string compactifications.


Gauge Theory Partition Function Modulus Space Fundamental Domain Heterotic String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • A. Shapere
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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