Advertisement

Physics of Atomic Nuclei

, Volume 76, Issue 6, pp 766–786 | Cite as

Calculation and modular properties of multiloop superstring amplitudes

  • G. S. DanilovEmail author
Elementary Particles and Fields Theory
  • 28 Downloads

Abstract

Multiloop superstring amplitudes are calculated within an extensively used gauge where the two-dimensional gravitino field carries Grassmann moduli. In general, the amplitudes possess, instead of modular symmetry, symmetry with respect to modular transformation supplemented with appropriate transformations of two-dimensional local supersymmetry. If the number of loops is larger than three, the integrationmeasures are notmodular forms, while the expression for the amplitude contains integrals along the boundary of the fundamental region of the modular group.

Keywords

Correlation Function Riemann Surface Atomic Nucleus Modular Form Zero Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. S. Danilov, Phys. Rev. D 51, 4359 (1995); Phys. Rev. D 52, 6201(E) (1995).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    G. S. Danilov, Phys. At. Nucl. 67, 1035 (2004).MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. A. Baranov and A. S. Shvarts, JETP Lett. 42, 419 (1985); D. Friedan, in Proceedings of the Santa Barbara Workshop on Unified String Theories, Ed. by D. Gross and M. Green (World Sci., Singapore, 1986).MathSciNetADSGoogle Scholar
  4. 4.
    P. Di Vecchia, K. Hornfeck, M. Frau, et al., Phys. Lett. B 211, 301 (1988); J. L. Petersen, J. R. Sidenius, and A. K. Tollst én, Phys. Lett. B 213, 30 (1988); Nucl. Phys. B 317, 109 (1989); B. E. W. Nilsson, A. K. Tollstén, and A. Wätterstam, Phys. Lett. B 222, 399 (1989).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    G. S. Danilov, JETP Lett. 58, 736 (1993); Class. Quantum Grav. 11, 2155 (1994).MathSciNetADSGoogle Scholar
  6. 6.
    N. Seiberg and E. Witten, Nucl. Phys. B 276, 272 (1986).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    J. J. Atick, G. W. Moore, and A. Sen, Nucl. Phys. B 307, 221 (1988).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    E. Verlinde and H. Verlinde, Phys. Lett. B 192, 95 (1987); Nucl. Phys B 288, 357 (1987).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    G.W. Moore and A. Morozov, Nucl. Phys. B 306, 387 (1988).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    E. D’Hoker and D. H. Phong, Phys. Lett. B 529, 241 (2002); Nucl. Phys. B 636, 3, 61 (2002); Nucl. Phys. B 639, 129 (2002); 715, 3, 91 (2005).MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    S. L. Cacciatori, F. Dalla Piazza, and B. van Geemen, Nucl. Phys. B 800, 565 (2008); Lett. Math. Phys. 85, 185 (2008); G. Grushevsky, Commun. Math. Phys. 287, 749 (2009); M. Oura, C. Poor, R. Salvati Manni, and D. S. Yuen, Math. Ann. 346, 477 (2010); M. Matone and R. Volpato, Nucl. Phys. B 732, 321 (2006).ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    P. Dunin-Barkowski, A. Morozov, and A. Sleptsov, J. High Energy Phys. 0910, 072 (2009).MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    M. Matone and R. Volpato, Nucl. Phys. B 839, 21 (2010).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    C. L. Siegal, Topics in Complex Function Theory (Wiley, New York, 1973), Vol. 3.Google Scholar
  15. 15.
    G. S. Danilov, Sov. J. Nucl. Phys. 52, 727 (1990); G. S. Danilov, Phys. Lett. B 257, 285 (1991).MathSciNetGoogle Scholar
  16. 16.
    A.M. Polyakov, Phys. Lett. B 103, 207, 210 (1981).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    G. S. Danilov, Nucl. Phys. B 463, 443 (1996).MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    J. Fay, Theta Functions on Riemann Surfaces, Lect. Notes Math., Vol. 352 (Springer, Berlin, New York, 1973).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Petersburg Nuclear Physics InstituteRussian Academy of SciencesGatchinaRussia

Personalised recommendations