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The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials.
1954
Earlier work this paper cites.
V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34
1972
Earlier work this paper cites.
M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53
1974
Earlier work this paper cites.
E. Brezin, C. Itzykson, G. Parisi and J. B. Zuber, “Planar Diagrams,” Commun. Math. Phys. 59
1978
Earlier work this paper cites.
D. J. Gross and E. Witten, “Possible Third Order Phase Transition In The Large N Lattice Gauge Theory,” Phys. Rev. D 21
1980
Earlier work this paper cites.
S. P. Hastings and J. B. McLeod, “A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation,” Arch. rational Mech. Anal. 73
1980
Earlier work this paper cites.
A. M. Polyakov, “Quantum geometry of bosonic strings,” Phys. Lett. B 103
1981
Earlier work this paper cites.
H. Flaschka and A. C. Newell, “Monodromy And Spectrum Preserving Deformations. 1,” Commun. Math. Phys. 76
1981
Earlier work this paper cites.
M. L. Mehta, “A Method Of Integration Over Matrix Variables,” Commun. Math. Phys. 79
1981
Earlier work this paper cites.
A. S. Fokas, A. R. Its, A. A. Kapaev and V. Y. Novokshenov, “Painlevé Transcendents: The Riemann-Hilbert Approach,” Mathematical Surveys and Monographs, Vol. 128 (2006) 553 pp; A. R. Its and V. Y. Novokshenov, “The Isomonodromic Deformation Method in the Theory of Painlevé Equations,” Springer-Verlag (1986)
1986
Earlier work this paper cites.
W. Wasow, “Asymptotic Expansions for Ordinary Differential Equations,” Interscience-Wiley, New York, 1985; Y. Sibuya, “Linear differential equations in the complex domain: problems of analytic continuation,” Translations of mathematical monographs, 82
1987
Earlier work this paper cites.
V. G. Knizhnik, A. M. Polyakov and A. B. Zamolodchikov, “Fractal structure of 2d-quantum gravity,” Mod. Phys. Lett. A 3
1988
Earlier work this paper cites.
F. David, “Conformal field theories coupled to 2-D gravity in the conformal gauge,” Mod. Phys. Lett. A 3
1989
Earlier work this paper cites.
V. A. Kazakov, “The Appearance of Matter Fields from Quantum Fluctuations of 2D Gravity,” Mod. Phys. Lett. A 4
1989
Earlier work this paper cites.
E. Brezin and V. A. Kazakov, “Exactly solvable field theories of closed strings,” Phys. Lett. B 236
1990
Earlier work this paper cites.
I. K. Kostov, “Strings embedded in Dynkin diagrams,” Cargese 1990, Proceedings, Random surfaces and quantum gravity, pp.135-149
1990
Earlier work this paper cites.
E. Brezin, E. Marinari and G. Parisi, “A Nonperturbative Ambiguity Free Solution Of A String Model,” Phys. Lett. B 242
1990
Earlier work this paper cites.
T. Banks, M. R. Douglas, N. Seiberg and S. H. Shenker, “Microscopic and macroscopic loops in nonperturbative two-dimensional gravity,” Phys. Lett. B 238
1990
Earlier work this paper cites.
E. Brezin, M. R. Douglas, V. Kazakov and S. H. Shenker, “The Ising model coupled to 2-d Gravity: A nonperturbative analysis,” Phys. Lett. B 237
1990
Earlier work this paper cites.
D. J. Gross and A. A. Migdal, “A nonperturbative treatment of two-dimensional quantum gravity,” Nucl. Phys. B 340
1990
Earlier work this paper cites.
M. R. Douglas, “Strings in less than one-dimension and the generalized KdV hierarchies,” Phys. Lett. B 238
1990
Earlier work this paper cites.
G. W. Moore, “Geometry Of The String Equations,” Commun. Math. Phys. 133
1990
Earlier work this paper cites.
P. H. Ginsparg and J. Zinn-Justin, “Action principle and large order behavior of nonperturbative gravity,” in Proceedings, Random Surfaces and Quantum Gravity, Cargese, 1990, pp. 85-109
1990
Earlier work this paper cites.
V. Periwal and D. Shevitz, “Unitary matrix models as exactly solvable string theories,” Phys. Rev. Lett. 64
1990
Earlier work this paper cites.
M. R. Douglas, N. Seiberg and S. H. Shenker, “Flow and instability in quantum gravity,” Phys. Lett. B 244
1990
Earlier work this paper cites.
C. R. Nappi, “Painleve-II And Odd Polynomials,” Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
S. H. Shenker, “The Strength of nonperturbative effects in string theory,” in Proceedings, Random Surfaces and Quantum Gravity, Cargese, 1990, pp. 191-200
1990
Earlier work this paper cites.
G. Bhanot, G. Mandal, O. Narayan, “Phase transitions in one matrix models,” Phys. Lett. B251
1990
Earlier work this paper cites.
V. Yu. Novokshenov, “The Boutroux ansatz for the second Painlevé equation in the complex domain,” Izv. Akad. Nauk SSSR Ser. Mat. 54
1990
Earlier work this paper cites.
I. K. Kostov, “Loop amplitudes for nonrational string theories,” Phys. Lett. B 266
1991
Earlier work this paper cites.
R. Dijkgraaf, H. L. Verlinde and E. P. Verlinde, “Loop Equations And Virasoro Constraints In Nonperturbative 2-D Quantum Gravity,” Nucl. Phys. B 348
1991
Earlier work this paper cites.
G. W. Moore, N. Seiberg and M. Staudacher, “From loops to states in 2-D quantum gravity,” Nucl. Phys. B 362
1991
Earlier work this paper cites.
C. Crnkovic and G. W. Moore, “Multicritical multicut matrix models,” Phys. Lett. B 257
1991
Cited alongside, same era.
I. K. Kostov, “Strings with discrete target space,” Nucl. Phys. B 376
1992
Cited alongside, same era.
T. Tada and M. Yamaguchi, “ P P and Q Q operator analysis for two matrix model,” Phys. Lett. B 250
1992
Cited alongside, same era.
M. Fukuma, H. Kawai and R. Nakayama, “Continuum Schwinger-Dyson equations and universal structures in two-dimensional quantum gravity,” Int. J. Mod. Phys. A 6
1992
Cited alongside, same era.
C. Crnkovic, M. R. Douglas and G. W. Moore, “Loop equations and the topological phase of multi-cut matrix models,” Int. J. Mod. Phys. A 7
1992
Cited alongside, same era.
P. Bleher and A. Its, “Double scaling limit in the random matrix model: the Riemann-Hilbert approach,” Communications on Pure and Applied Mathematics, 56 (2003) 433-516 [arXiv:math-ph/0201003]
2003
Later among the works it cites.
M. Sato, RIMS Kokyuroku 439
2003
Later among the works it cites.
S. Dalley, C. V. Johnson, T. R. Morris and A. Watterstam, “Unitary matrix models and 2-D quantum gravity,” Mod. Phys. Lett. A 7
2003
Later among the works it cites.
N. Seiberg and D. Shih, “Branes, rings and matrix models in minimal (super)string theory,” JHEP 0402
2004
Later among the works it cites.
I. R. Klebanov, J. M. Maldacena and N. Seiberg, “Unitary and complex matrix models as 1-d type 0 strings,” Commun. Math. Phys. 252
2004
Later among the works it cites.
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T. J. Hollowood, L. Miramontes, A. Pasquinucci and C. Nappi, “Hermitian Versus Anti-Hermitian One Matrix Models And Their Hierarchies,” Nucl. Phys. B 373
1992
Cited alongside, same era.
N. Seiberg and S. H. Shenker, “A Note on background (in)dependence,” Phys. Rev. D 45
1992
Cited alongside, same era.
A. S. Fokas and M. J. Ablowitz, “On the initial value problem of the second Painlevé transcendent,” Comm. Math. Phys. 91
1992
Cited alongside, same era.
S. Dalley, C. V. Johnson and T. R. Morris, “Multicritical Complex Matrix Models And Nonperturbative 2-D Quantum Gravity,” Nucl. Phys. B 368
1992
Cited alongside, same era.
M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Commun. Math. Phys. 147
1992
Cited alongside, same era.
B. Eynard and J. Zinn-Justin, “Large order behavior of 2-D gravity coupled to d < 1 d<1 matter,” Phys. Lett. B 302
1993
Cited alongside, same era.
F. David, “Phases of the large N matrix model and nonperturbative effects in 2-d gravity,” Nucl. Phys. B 348
1993
Cited alongside, same era.
J. M. Maldacena, G. W. Moore, N. Seiberg and D. Shih, “Exact vs. semiclassical target space of the minimal string,” JHEP 0410
2004
Later among the works it cites.
B. Eynard, “Topological expansion for the 1-hermitian matrix model correlation functions,” JHEP 0411
2004
Later among the works it cites.
M. Hanada, M. Hayakawa, N. Ishibashi, H. Kawai, T. Kuroki, Y. Matsuo and T. Tada, “Loops versus matrices: The nonperturbative aspects of noncritical string,” Prog. Theor. Phys. 112
2004
Later among the works it cites.
D. Kutasov, K. Okuyama, J. w. Park, N. Seiberg and D. Shih, “Annulus amplitudes and ZZ branes in minimal string theory,” JHEP 0408
2004
Later among the works it cites.
N. Seiberg and D. Shih, “Flux vacua and branes of the minimal superstring,” JHEP 0501
2005
Later among the works it cites.
H. Kawai, T. Kuroki and Y. Matsuo, “Universality of nonperturbative effect in type 0 string theory,” Nucl. Phys. B 711
2005
Later among the works it cites.
R. de Mello Koch, A. Jevicki and J. P. Rodrigues, “Instantons in c = 0 CSFT,” JHEP 0504
2005
Later among the works it cites.
A. Sato and A. Tsuchiya, “ZZ brane amplitudes from matrix models,” JHEP 0502
2005
Later among the works it cites.
N. Ishibashi and A. Yamaguchi, “On the chemical potential of D-instantons in c = 0 noncritical string theory,” JHEP 0506
2005
Later among the works it cites.
M. Fukuma, H. Irie and S. Seki, “Comments on the D-instanton calculus in ( p , p + 1 ) (p,p+1) minimal string theory,” Nucl. Phys. B 728
2005
Later among the works it cites.
M. Fukuma, H. Irie and Y. Matsuo, “Notes on the algebraic curves in ( p , q ) (p,q) minimal string theory,” JHEP 0609
2006
Later among the works it cites.
Y. Matsuo, “Nonperturbative effect in c = 1 noncritical string theory and Penner model,” Nucl. Phys. B 740
2006
Later among the works it cites.
T. Claeys, A. B. J. Kuijlaars “Universality of the double scaling limit in random matrix models,” Comm. Pure Appl. Math. 59 (2006), 1573 [arXiv:math-ph/0501074]
2006
Later among the works it cites.
P. Horava and C. A. Keeler, “Noncritical M-theory in 2+1 dimensions as a nonrelativistic Fermi liquid,” JHEP 0707
2007
Later among the works it cites.
M. Fukuma and H. Irie, “A string field theoretical description of ( p , q ) (p,q) minimal superstrings,” JHEP 0701
2007
Later among the works it cites.
T. Kuroki and F. Sugino, “T-duality of ZZ-brane,” arXiv:hep-th/0612042; “T duality of the Zamolodchikov-Zamolodchikov brane,” Phys. Rev. D 75
2007
Later among the works it cites.
M. Fukuma and H. Irie, “Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories,” JHEP 0703
2007
Later among the works it cites.
2008
Later among the works it cites.
2009
Later among the works it cites.
2009
Later among the works it cites.
M. Marino, R. Schiappa and M. Weiss, “Multi-Instantons and Multi-Cuts,” J. Math. Phys. 50
2009
Later among the works it cites.
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M. Marino, “Non-Perturbative effects in Matrix model, Chern-Simons Theory and Topological Strings,” lectures in conference, Topological Strings, Modularity and non-perturbative Physics
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C. -T. Chan, H. Irie, C. -H. Yeh, “Stokes Phenomena and Integrable Structures in Non-critical String/M Theory,” in preparation; a talk in Gong Show, Strings 2011, Uppsala June 27 - July 2
2011
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