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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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).
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.
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.
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.
F. David, Mod. Phys. Lett. A5 (1990) 1019.
F. David, Saclay preprint, July 1990, SPhT/90–090.
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.
E. Brézin, E. Marinari and G. Parisi, Phys. Lett. B242 (1990) 35.
E. Brézin, C. Itzykson, G. Parisi and J. Zuber, Comm Math. Phys. 59 (1978) 35.
E. Marinari and G. Parisi, Phys. Lett. B240 (1990) 375.
T. Banks, N. Seiberg and S. Shenker, unpublished.
M. Karliner and A. Migdal, Princeton preprint, July 1990.
G. Parisi, presentation at the Cargèse workshop.
P. Ginsparg and J. Zinn-Justin, presentation at the Cargèse workshop.
D. Gross and V. Periwal, Phys. Rev. Lett. 60 (1988) 2105.
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].
E. Witten, Nucl. Phys. B268 (1986) 253; S. B. Giddings, E. Martinec and E. Witten, Phys. Lett. B176 (1986) 362.
J. Harer and D. Zagier, Inv. Math. 185 (1986) 457; R. Penner, Comm. Math. Phys. 113 (1987) 299; J. Diff. Geom. 27 (1988) 35.
D. Bessis, C. Itzykson and J.-B. Zuber, Adv. Appl. Math. 1 (1980) 109.
C. Itzykson and J.-B. Zuber, Saclay preprint, January 1990, SPhT/90–004.
E. D’Hoker and D. Phong, Nucl. Phys. B269 (1986) 205.
R. Penner, Institut Mittag-Leffler preprint no. 10, 1989.
E. Witten, IAS preprint, May 1990.
J. Horne, Princeton preprint June 1990, PUPT-1185.
D. Kutasov and N. Seiberg, Rutgers preprint, July 1990.
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.
S. Das and A. Jevicki, Brown preprint, 1990; J. Polchinski, Texas preprint, 1990, UTTG-15–90.
T. Banks, presentation at the Cargèse workshop.
E. Witten, Nucl. Phys. B156 (1979) 269.
V. Periwal and D. Shevitz, Phys. Rev. Lett. 64 (1990) 1326.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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