Skip to main content

The Strength of Nonperturbative Effects in String Theory

  • Chapter
Book cover Random Surfaces and Quantum Gravity

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

Abstract

We argue that the leading weak coupling nonperturbative effects in closed string theories should be of order exp(— C/κ) where κ 2 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/κ 2 ) 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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. 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. 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. 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. 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. F. David, Mod. Phys. Lett. A5 (1990) 1019.

    ADS  Google Scholar 

  7. F. David, Saclay preprint, July 1990, SPhT/90–090.

    Google Scholar 

  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. E. Brézin, E. Marinari and G. Parisi, Phys. Lett. B242 (1990) 35.

    ADS  Google Scholar 

  10. E. Brézin, C. Itzykson, G. Parisi and J. Zuber, Comm Math. Phys. 59 (1978) 35.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. E. Marinari and G. Parisi, Phys. Lett. B240 (1990) 375.

    MathSciNet  ADS  Google Scholar 

  12. T. Banks, N. Seiberg and S. Shenker, unpublished.

    Google Scholar 

  13. M. Karliner and A. Migdal, Princeton preprint, July 1990.

    Google Scholar 

  14. G. Parisi, presentation at the Cargèse workshop.

    Google Scholar 

  15. P. Ginsparg and J. Zinn-Justin, presentation at the Cargèse workshop.

    Google Scholar 

  16. D. Gross and V. Periwal, Phys. Rev. Lett. 60 (1988) 2105.

    Article  MathSciNet  ADS  Google Scholar 

  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. E. Witten, Nucl. Phys. B268 (1986) 253; S. B. Giddings, E. Martinec and E. Witten, Phys. Lett. B176 (1986) 362.

    Google Scholar 

  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. D. Bessis, C. Itzykson and J.-B. Zuber, Adv. Appl. Math. 1 (1980) 109.

    Article  MathSciNet  MATH  Google Scholar 

  21. C. Itzykson and J.-B. Zuber, Saclay preprint, January 1990, SPhT/90–004.

    Google Scholar 

  22. E. D’Hoker and D. Phong, Nucl. Phys. B269 (1986) 205.

    Article  MathSciNet  ADS  Google Scholar 

  23. R. Penner, Institut Mittag-Leffler preprint no. 10, 1989.

    Google Scholar 

  24. E. Witten, IAS preprint, May 1990.

    Google Scholar 

  25. J. Horne, Princeton preprint June 1990, PUPT-1185.

    Google Scholar 

  26. D. Kutasov and N. Seiberg, Rutgers preprint, July 1990.

    Google Scholar 

  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. S. Das and A. Jevicki, Brown preprint, 1990; J. Polchinski, Texas preprint, 1990, UTTG-15–90.

    Google Scholar 

  29. T. Banks, presentation at the Cargèse workshop.

    Google Scholar 

  30. E. Witten, Nucl. Phys. B156 (1979) 269.

    Article  MathSciNet  ADS  Google Scholar 

  31. V. Periwal and D. Shevitz, Phys. Rev. Lett. 64 (1990) 1326.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Shenker, S.H. (1991). The Strength of Nonperturbative Effects in String Theory. In: Alvarez, O., Marinari, E., Windey, P. (eds) Random Surfaces and Quantum Gravity. NATO ASI Series, vol 262. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3772-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-3772-4_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6681-2

  • Online ISBN: 978-1-4615-3772-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics