Modular Invariance of Field Theories and String Compactifications

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

Abstract

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.

Keywords

Dine 

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References

  1. [1]
    H.A. Kramers and G.H. Wannier, Phys.Rev. 60, (1941) 252.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    J. Cardy, Nucl. Phys. B205 (1982) 17.MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    J. Cardy and E. Rabinovici, Nucl. Phys. B205 (1982)Google Scholar
  4. [4]
    J.V. José, L.P. Kadanoff, S. Kirkpatrick, D.R. Nelson, Phys. Rev. 16 (1977) 1217.ADSCrossRefGoogle Scholar
  5. [5]
    A. Shapere and F. Wilczek, “Self-Dual Models with Theta Terms,” Nucl. Phys. B320 (1989) 669.MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    R. Savit, Rev. Mod. Phys. 52 (1980) 453.MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    G. ‘t Hooft, Nucl. Phys. B190 (1981) 455.Google Scholar
  8. [8]
    D. Mumford, Tata Lectures on Theta, vol. I (Birkhauser, 1983 ).Google Scholar
  9. [9]
    K. Kikkawa and M. Yamasaki, Phys.Lett. 149B, (1984) 357.MathSciNetCrossRefGoogle Scholar
  10. [10]
    V.P. Nair, A. Shapere, A. Strominger, F. Wilczek, Nucl. Phys. B287 (1987) 414.MathSciNetCrossRefGoogle Scholar
  11. [11]
    K.S. Narain, Phys. Lett. 169B (1986) 41.MathSciNetCrossRefGoogle Scholar
  12. [12]
    K.S. Narain, M.H. Sarmadi, E. Witten, Nucl. Phys. B279 (1987) 369.MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    R. Dijkgraaf, E. Verlinde and H. Verlinde, Comm. Math. Phys. 115 (1988) 649.MathSciNetADSMATHCrossRefGoogle Scholar
  14. [14]
    P. Ginsparg and C. Vafa, Nucl. Phys. B289 (1987) 414.MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    M. Dine, P. Huet, and N. Seiberg, City College of New York preprint HEP- 88/20.Google Scholar
  16. [16]
    S. Ferrara, A. Shapere, D. Lüst, and S. Theisen, “Modular Invariance in Supersymmetric Field Theories,” to appear in Physics Letters B.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

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

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