Abstract
We study the effect of ZZ instantons in c = 1 string theory, and demonstrate that they give rise to non-perturbative corrections to scattering amplitudes that do not saturate unitarity within the closed string sector. Beyond the leading non-perturbative order, logarithmic divergences are canceled between worldsheet diagrams of different topologies, due to the Fischler-Susskind-Polchinski mechanism. We propose that the closed string vacuum in c = 1 string theory is non-perturbatively dual to a state of the matrix quantum mechanics in which all scattering states up to a given energy with no incoming flux from the “other side” of the potential are occupied by free fermions. Under such a proposal, we find detailed agreement of non-perturbative corrections to closed string amplitudes in the worldsheet description and in the dual matrix model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.R. Klebanov, String theory in two-dimensions, in the proceedings of the Spring School on String Theory and Quantum Gravity (to be followed by Workshop), Trieste, Italy, April 15–23 (1991) [hep-th/9108019] [INSPIRE].
P.H. Ginsparg and G.W. Moore, Lectures on 2-D gravity and 2-D string theory, in the proceedings of the Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, Boulder, Colorado, June 3–28 1993, p. 277–469 [hep-th/9304011] [INSPIRE].
A. Jevicki, Development in 2-d string theory, in the proceedings of the Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste, Italy, April 28–29 1993 [https://doi.org/10.1142/9789814447072_0004] [hep-th/9309115] [INSPIRE].
J. Polchinski, What is string theory?, in the proceedings of the NATO Advanced Study Institute: Les Houches Summer School, Session 62: Fluctuating Geometries in Statistical Mechanics and Field Theory, Les Houches, France, August 2 – September 9 1994 [hep-th/9411028] [INSPIRE].
E.J. Martinec, Matrix models and 2D string theory, in the proceedings of the NATO Advanced Study Institute: Marie Curie Training Course: Applications of Random Matrices in Physics, Vancouver, Canada, August 2–13 2004, p. 403–457 [hep-th/0410136] [INSPIRE].
G.W. Moore, M.R. Plesser and S. Ramgoolam, Exact S matrix for 2-D string theory, Nucl. Phys. B 377 (1992) 143 [hep-th/9111035] [INSPIRE].
P. Di Francesco and D. Kutasov, Correlation functions in 2-D string theory, Phys. Lett. B 261 (1991) 385 [INSPIRE].
P. Di Francesco and D. Kutasov, World sheet and space-time physics in two-dimensional (Super)string theory, Nucl. Phys. B 375 (1992) 119 [hep-th/9109005] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, The c = 1 string theory S-matrix revisited, JHEP 04 (2019) 145 [arXiv:1705.07151] [INSPIRE].
J.M. Maldacena, Long strings in two dimensional string theory and non-singlets in the matrix model, JHEP 09 (2005) 078 [hep-th/0503112] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, Long String Scattering in c = 1 String Theory, JHEP 01 (2019) 173 [arXiv:1810.07233] [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. 1. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, PoS tmr2000 (2000) 041 [hep-th/0009138] [INSPIRE].
J. McGreevy and H.L. Verlinde, Strings from tachyons: The c=1 matrix reloaded, JHEP 12 (2003) 054 [hep-th/0304224] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) R6041 [hep-th/9407031] [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance, Phys. Lett. B 171 (1986) 383 [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance. 2, Phys. Lett. B 173 (1986) 262 [INSPIRE].
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
A. Sen, Rolling tachyon, JHEP 04 (2002) 048 [hep-th/0203211] [INSPIRE].
A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [INSPIRE].
T. Takayanagi and N. Toumbas, A Matrix model dual of type 0B string theory in two-dimensions, JHEP 07 (2003) 064 [hep-th/0307083] [INSPIRE].
M.R. Douglas et al., A New hat for the c=1 matrix model, hep-th/0307195 [INSPIRE].
J. Polchinski, Dirichlet Branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
H. Dorn and H.J. Otto, Two and three point functions in Liouville theory, Nucl. Phys. B 429 (1994) 375 [hep-th/9403141] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [INSPIRE].
M. Cho, S. Collier and X. Yin, Recursive Representations of Arbitrary Virasoro Conformal Blocks, JHEP 04 (2019) 018 [arXiv:1703.09805] [INSPIRE].
A.D. Sokal, An improvement of Watson’s theorem on Borel summability, J. Math. Phys. 21 (1980) 261 [INSPIRE].
F. Nevanlinna, Zur Theorie der asymptotischen Potenzreihen, Ann. Acad. Sci. Fenn. Ser. A 12 (1918–19).
J. Polchinski, On the nonperturbative consistency of d = 2 string theory, Phys. Rev. Lett. 74 (1995) 638 [hep-th/9409168] [INSPIRE].
B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241] [INSPIRE].
A.B. Zamolodchikov, Conformal symmetry in two-dimensions: an explicit recurrence formula for the conformal partial wave amplitude, Commun. Math. Phys. 96 (1984) 419 [INSPIRE].
Acknowledgments
We would like to thank Igor Klebanov, Juan Maldacena, Ashoke Sen, Marco Serone, Steve Shenker, Andy Strominger, and Yifan Wang for discussions. BB and VR thank the organizers of Bootstrap 2019 at Perimeter Institute, VR thanks the organizers of Strings 2019, Brussels, XY thanks the Galileo Galilei Institute for Theoretical Physics, Florence, the Center for Quantum Mathematics and Physics at University of California, Davis, International Center for Theoretical Physics, Trieste, and Nordic Institute for Theoretical Physics, Stockholm, for their hospitality during the course of this work. This work is supported in part by a Simons Investigator Award from the Simons Foundation, by the Simons Collaboration Grant on the Non-Perturbative Bootstrap, and by DOE grant DE-SC00007870. BB is supported by the Bolsa de Doutoramento FCT fellowship. VR is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1144152.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1907.07688
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Balthazar, B., Rodriguez, V.A. & Yin, X. ZZ instantons and the non-perturbative dual of c = 1 string theory. J. High Energ. Phys. 2023, 48 (2023). https://doi.org/10.1007/JHEP05(2023)048
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)048