Random Surfaces and Quantum Gravity pp 191-200

Part of the NATO ASI Series book series (NSSB, volume 262)

The Strength of Nonperturbative Effects in String Theory

  • Stephen H. Shenker

Abstract

We argue that the leading weak coupling nonperturbative effects in closed string theories should be of order exp(— C/κ) where κ2 is the closed string coupling constant. This is the case in the exactly soluble matrix models. These effects are in principle much larger than the exp(—C/κ2) effects typical of the low energy field theory. We argue that this behavior should be generic in string theory because string perturbation theory generically behaves like (2g)! at genus g.

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References

  1. [1]
    E. Brézin and V. Kazakov, Phys. Lett. B236 (1990) 144; M. Douglas and S. Shenker, Nucl. Phys. B335 (1990) 635; D. Gross and A. Migdal, Phys. Rev. Lett. 64 (1990) 127.Google Scholar
  2. [2]
    E. Brézin, M. Douglas, V. Kazakov and S. Shenker Phys. Lett. B237 (1990) 43; C. Crnkovié, P. Ginsparg and G. Moore Phys. Lett. B237 (1990) 196; D. Gross and A. Migdal, Phys. Rev. Lett. 64 (1990) 717; T. Banks, M. R. Douglas, N. Seiberg and S. Shenker, Phys. Lett. B238 (1990) 279; D. Gross and A. Migdal, Nucl. Phys. B340 (1990) 333; M. Douglas, Phys. Lett. B238 (1990) 176; P. Di Francesco and D. Kutasov, Princeton preprint PUPT-1173 (1990).Google Scholar
  3. [3]
    E. Brézin, V. Kazakov and Al. Zamolodchikov, Ecole Normale preprint, December 1989, LPS-ENS 89–182, Nucl. Phys. B (in press); P. Ginsparg and J. Zinn-Justin, Phys. Lett. B240 (1990) 333; D. Gross and N. Miljkovié, Phys. Lett. B238 (1990) 217; G. Parisi, Phys. Lett. B238 (1990) 209; G. Parisi, Phys. Lett. B238 (1990) 213; D. Gross and I. Klebanov, Princeton preprint, March 1990, PUPT-1172.Google Scholar
  4. [4]
    J. Ambjorn, B. Durhuus and J. Fröhlich, Nucl. Phys. B257 (1985) 433; F. David, Nucl. Phys. B257 (1985)45; V. Kazakov, Phys. Lett. B150 (1985) 282; V. Kazakov, I. Kostov and A. Migdal Phys. Lett. B157 (1985) 295.Google Scholar
  5. [5]
    E. Witten, Nucl. Phys. B340 (1990) 281; J Distler, Princeton preprint, 1990 PUPT-1161; R. Dijkgraaf and E. Witten, IAS preprint, February 1990; E. Ver-linde and H. Verlinde, IAS preprint, April 1990; R. Dijkgraaf, E. Verlinde and H. Verlinde, IAS preprint, May 1990.Google Scholar
  6. [6]
    F. David, Mod. Phys. Lett. A5 (1990) 1019.ADSGoogle Scholar
  7. [7]
    F. David, Saclay preprint, July 1990, SPhT/90–090.Google Scholar
  8. [8]
    M. Douglas, N. Seiberg, and S. Shenker, Rutgers preprint, April 1990, Phys. Lett. B (in press). For rigorous results see G. Moore, Yale preprint, April 1990.Google Scholar
  9. [9]
    E. Brézin, E. Marinari and G. Parisi, Phys. Lett. B242 (1990) 35.ADSGoogle Scholar
  10. [10]
    E. Brézin, C. Itzykson, G. Parisi and J. Zuber, Comm Math. Phys. 59 (1978) 35.MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    E. Marinari and G. Parisi, Phys. Lett. B240 (1990) 375.MathSciNetADSGoogle Scholar
  12. [12]
    T. Banks, N. Seiberg and S. Shenker, unpublished.Google Scholar
  13. [13]
    M. Karliner and A. Migdal, Princeton preprint, July 1990.Google Scholar
  14. [14]
    G. Parisi, presentation at the Cargèse workshop.Google Scholar
  15. [15]
    P. Ginsparg and J. Zinn-Justin, presentation at the Cargèse workshop.Google Scholar
  16. [16]
    D. Gross and V. Periwal, Phys. Rev. Lett. 60 (1988) 2105.MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    The link between the (2g)! growth of perturbation theory in the matrix models and the number of cells in the moduli space was first made by Douglas and the author in [1].Google Scholar
  18. [18]
    E. Witten, Nucl. Phys. B268 (1986) 253; S. B. Giddings, E. Martinec and E. Witten, Phys. Lett. B176 (1986) 362.Google Scholar
  19. [19]
    J. Harer and D. Zagier, Inv. Math. 185 (1986) 457; R. Penner, Comm. Math. Phys. 113 (1987) 299; J. Diff. Geom. 27 (1988) 35.Google Scholar
  20. [20]
    D. Bessis, C. Itzykson and J.-B. Zuber, Adv. Appl. Math. 1 (1980) 109.MathSciNetMATHCrossRefGoogle Scholar
  21. [21]
    C. Itzykson and J.-B. Zuber, Saclay preprint, January 1990, SPhT/90–004.Google Scholar
  22. [22]
    E. D’Hoker and D. Phong, Nucl. Phys. B269 (1986) 205.MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    R. Penner, Institut Mittag-Leffler preprint no. 10, 1989.Google Scholar
  24. [24]
    E. Witten, IAS preprint, May 1990.Google Scholar
  25. [25]
    J. Horne, Princeton preprint June 1990, PUPT-1185.Google Scholar
  26. [26]
    D. Kutasov and N. Seiberg, Rutgers preprint, July 1990.Google Scholar
  27. [27]
    M. Kaku, in Functional Integration, Geometry and Strings,Z. Haba and J. Sobczyk, eds. Berlin (1989); T. Kugo, H. Kumitomo and K. Suehiro, Phys. Lett. B226 (1989) 48; M. Saadi and B. Zweibach, Ann. Phys. 192(1989)213.Google Scholar
  28. [28]
    S. Das and A. Jevicki, Brown preprint, 1990; J. Polchinski, Texas preprint, 1990, UTTG-15–90.Google Scholar
  29. [29]
    T. Banks, presentation at the Cargèse workshop.Google Scholar
  30. [30]
    E. Witten, Nucl. Phys. B156 (1979) 269.MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    V. Periwal and D. Shevitz, Phys. Rev. Lett. 64 (1990) 1326.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Stephen H. Shenker
    • 1
  1. 1.Department of Physics and AstronomyRutgers UniversityPiscatawayUSA

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