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Twisted modular forms and Atkin-Lehner symmetries

Abstract

A new “stringy” symmetry leading to zero cosmological constant to one loop is introduced. The partition function is a modular function which gets multiplied by a certain group character under modular transformations. The elementary fact that the sum over group elements of any nontrivial character is zero gives the desired result. The relationship of this symmetry with Moore's Atkin-Lehner transformations, as well as with Gross and Mende's analysis of anomalous heterotic strings is clarified. General classes of two dimensional models are also investigated.

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References

  1. P. Ginsparg, C. Vafa: Nucl. Phys. B289 (1987) 414

    Google Scholar 

  2. G. Moore: Nucl. Phys. B293 (1987) 139; G. Moore: Vanishing vacuum energies for non supersymmetric string. IASSNS-HEP-87/59

    Google Scholar 

  3. N. Koblitz: Introduction to elliptic curves and modular forms Berlin, Heidelberg, New York: Springer 1984; B. Schoeneberg: Elliptic modular forms: an introduction Berlin, Heidelberg, New York: Springer 1974; S. Lang: Introduction to modular forms. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  4. D.J. Gross, P.F. Mende: Nucl. Phys. B291 (1987) 653

    Google Scholar 

  5. E. Álvarez, M.A.R. Osorio: Nucl. Phys. B304 (1988) 327

    Google Scholar 

  6. T.R. Taylor: preprint FERMILAB-pub-87/157-T

  7. Z.I. Borevich, I.R. Shafarevich: Number theory, London, New York: Academic Press 1966; N. Koblitz: A course in number theory and crystalography Berlin, Heidelberg, New York: Springer 1987; J.P. Serre: A course in arithmetic Berlin, Heidelberg, New York: Springer 1977; J. Conway, P. Norton: Bull. Lond. Math. Soc. 11 (1979) 308

    Google Scholar 

  8. J. Harvey: Twisting the heterotic string in: Unified string theories, D.J. Gross (ed.), Singapore: World Scientific 1986

    Google Scholar 

  9. A.N. Reidlich, K. Tsokos: String partition functions on the Niemeier lattices. Brandeis preprint, BRX-TH212

  10. L.J. Dixon, J.A. Harvey: Nucl. Phys. B279 (1986) 93

    Google Scholar 

  11. H.J. Schnitzer, K. Tsokos: Partition functions and Fermi-Bose equivalence for simply-laced groups Brandeis preprint, BRX-TH215

  12. D. Mumford: Tata lectures on theta. Basel, Boston, Stuttgart: Birkhäuser 1983

    Google Scholar 

  13. L. Álvarez-Gaumé, C. Gómez, G. Moore, C. Vafa: preprint CERNTH-4883/87

  14. E. Álvarez, M.A.R. Osorio: Phys. Rev. D36 (1987) 1175

    Google Scholar 

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Álvarez, E., Osorio, M.A.R. Twisted modular forms and Atkin-Lehner symmetries. Z. Phys. C - Particles and Fields 44, 89–96 (1989). https://doi.org/10.1007/BF01548586

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  • DOI: https://doi.org/10.1007/BF01548586

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Partition Function
  • Cosmological Constant