Abstract
We compute the normalization of the general multi-instanton contribution to the partition function of (p′, p) minimal string theory and also to the dual two-matrix integral. We find perfect agreement between the two results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2 − D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].
N. Seiberg and D. Shih, Minimal string theory, C. R. Phys. 6 (2005) 165 [hep-th/0409306] [INSPIRE].
S.H. Shenker, The Strength of nonperturbative effects in string theory, in Cargese Study Institute: Random Surfaces, Quantum Gravity and Strings, Cargese, France (1990), pg. 809.
F. David, Phases of the large N matrix model and nonperturbative effects in 2 − D gravity, Nucl. Phys. B 348 (1991) 507 [INSPIRE].
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) R6041 [hep-th/9407031] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, ZZ Instantons and the Non-Perturbative Dual of c = 1 String Theory, arXiv:1907.07688 [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, Multi-Instanton Calculus in c = 1 String Theory, arXiv:1912.07170 [INSPIRE].
A. Sen, Normalization of D-instanton amplitudes, JHEP 11 (2021) 077 [arXiv:2101.08566] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, The S-matrix of 2D Type 0B String Theory. Part 2: D-Instanton Effects, arXiv:2204.01747 [INSPIRE].
A. Sen, Normalization of type IIB D-instanton amplitudes, JHEP 12 (2021) 146 [arXiv:2104.11109] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, D-instantons in Type IIA string theory on Calabi-Yau threefolds, JHEP 11 (2021) 018 [arXiv:2108.04265] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds, JHEP 12 (2021) 044 [arXiv:2110.06949] [INSPIRE].
S. Alexandrov, A.H. Fırat, M. Kim, A. Sen and B. Stefański, D-instanton induced superpotential, JHEP 07 (2022) 090 [arXiv:2204.02981] [INSPIRE].
N.B. Agmon, B. Balthazar, M. Cho, V.A. Rodriguez and X. Yin, D-instanton Effects in Type IIB String Theory, arXiv:2205.00609 [INSPIRE].
D.S. Eniceicu, R. Mahajan, C. Murdia and A. Sen, Normalization of ZZ instanton amplitudes in minimal string theory, JHEP 07 (2022) 139 [arXiv:2202.03448] [INSPIRE].
E.J. Martinec, The Annular report on noncritical string theory, hep-th/0305148 [INSPIRE].
D. Kutasov, K. Okuyama, J.-w. Park, N. Seiberg and D. Shih, Annulus amplitudes and ZZ branes in minimal string theory, JHEP 08 (2004) 026 [hep-th/0406030] [INSPIRE].
F. David, Nonperturbative effects in matrix models and vacua of two-dimensional gravity, Phys. Lett. B 302 (1993) 403 [hep-th/9212106] [INSPIRE].
A. Sato and A. Tsuchiya, ZZ brane amplitudes from matrix models, JHEP 02 (2005) 032 [hep-th/0412201] [INSPIRE].
M. Hanada et al., Loops versus matrices: The Nonperturbative aspects of noncritical string, Prog. Theor. Phys. 112 (2004) 131 [hep-th/0405076] [INSPIRE].
N. Ishibashi and A. Yamaguchi, On the chemical potential of D-instantons in c=0 noncritical string theory, JHEP 06 (2005) 082 [hep-th/0503199] [INSPIRE].
N. Ishibashi, T. Kuroki and A. Yamaguchi, Universality of nonperturbative effects in c < 1 noncritical string theory, JHEP 09 (2005) 043 [hep-th/0507263] [INSPIRE].
M. Mariño, R. Schiappa and M. Weiss, Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings, Commun. Num. Theor. Phys. 2 (2008) 349 [arXiv:0711.1954] [INSPIRE].
M. Mariño, R. Schiappa and M. Weiss, Multi-Instantons and Multi-Cuts, J. Math. Phys. 50 (2009) 052301 [arXiv:0809.2619] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
M. Mariño, Lectures on non-perturbative effects in large N gauge theories, matrix models and strings, Fortsch. Phys. 62 (2014) 455 [arXiv:1206.6272] [INSPIRE].
G.V. Dunne and M. Ünsal, What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles, PoS LATTICE2015 (2016) 010 [arXiv:1511.05977] [INSPIRE].
I. Aniceto, G. Basar and R. Schiappa, A Primer on Resurgent Transseries and Their Asymptotics, Phys. Rept. 809 (2019) 1 [arXiv:1802.10441] [INSPIRE].
A. Sen, Universality of the tachyon potential, JHEP 12 (1999) 027 [hep-th/9911116] [INSPIRE].
A. Sen and B. Zwiebach, Tachyon condensation in string field theory, JHEP 03 (2000) 002 [hep-th/9912249] [INSPIRE].
M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys. 10 (2006) 433 [hep-th/0511286] [INSPIRE].
T. Erler and C. Maccaferri, String field theory solution for any open string background. Part II, JHEP 01 (2020) 021 [arXiv:1909.11675] [INSPIRE].
A. Sen, SO(32) spinors of type-I and other solitons on brane - anti-brane pair, JHEP 09 (1998) 023 [hep-th/9808141] [INSPIRE].
E. Witten, D-branes and k-theory, JHEP 12 (1998) 019 [hep-th/9810188] [INSPIRE].
N. Berkovits, A. Sen and B. Zwiebach, Tachyon condensation in superstring field theory, Nucl. Phys. B 587 (2000) 147 [hep-th/0002211] [INSPIRE].
V.A. Kazakov and I.K. Kostov, Instantons in noncritical strings from the two matrix model, in From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, Oxford, U.K. (2004), pg. 1864 [hep-th/0403152] [INSPIRE].
R. Schiappa and R. Vaz, The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation, Commun. Math. Phys. 330 (2014) 655 [arXiv:1302.5138] [INSPIRE].
A. Sen, Muti-instanton amplitudes in type IIB string theory, JHEP 12 (2021) 065 [arXiv:2104.15110] [INSPIRE].
J.L. Cardy, Boundary Conditions, Fusion Rules and the Verlinde Formula, Nucl. Phys. B 324 (1989) 581 [INSPIRE].
N. Seiberg and D. Shih, Branes, rings and matrix models in minimal (super)string theory, JHEP 02 (2004) 021 [hep-th/0312170] [INSPIRE].
M.R. Douglas, The Two matrix model, in Cargese Study Institute: Random Surfaces, Quantum Gravity and Strings, Cargese, France (1990), pg. 77.
J.M. Daul, V.A. Kazakov and I.K. Kostov, Rational theories of 2 − D gravity from the two matrix model, Nucl. Phys. B 409 (1993) 311 [hep-th/9303093] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997), https://doi.org/10.1007/978-1-4612-2256-9 [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press (12, 2007), https://doi.org/10.1017/CBO9780511816079 [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
M. Marcos, International series of monographs on physics. Vol. 131: Chern-Simons Theory, Matrix Models, and Topological Strings, Clarendon Press (2005) [ISBN:9780198568490].
E. Brézin, C. Itzykson, G. Parisi and J.B. Zuber, Planar Diagrams, Commun. Math. Phys. 59 (1978) 35 [INSPIRE].
D. Bessis, C. Itzykson and J.B. Zuber, Quantum field theory techniques in graphical enumeration, Adv. Appl. Math. 1 (1980) 109 [INSPIRE].
N. . Ercolani and K.D. T.-R. McLaughlin, Asymptotics of the partition function for random matrices via riemann-hilbert techniques and applications to graphical enumeration, Int. Math. Res. Not. 2003 (2003) 755 [math-ph/0211022].
G.W. Moore, N. Seiberg and M. Staudacher, From loops to states in 2 − D quantum gravity, Nucl. Phys. B 362 (1991) 665 [INSPIRE].
R. Mahajan, D. Stanford and C. Yan, Sphere and disk partition functions in Liouville and in matrix integrals, JHEP 07 (2022) 132 [arXiv:2107.01172] [INSPIRE].
S.Y. Alexandrov, V.A. Kazakov and D. Kutasov, Nonperturbative effects in matrix models and D-branes, JHEP 09 (2003) 057 [hep-th/0306177] [INSPIRE].
Harish-Chandra, Differential Operators on a Semisimple Lie Algebra, Am. J. Math. 79 (1957) 87 [INSPIRE].
C. Itzykson and J.B. Zuber, The Planar Approximation. 2, J. Math. Phys. 21 (1980) 411 [INSPIRE].
P. Zinn-Justin and J.B. Zuber, On some integrals over the U(N) unitary group and their large N limit, J. Phys. A 36 (2003) 3173 [math-ph/0209019] [INSPIRE].
M.L. Mehta, A Method of Integration Over Matrix Variables, Commun. Math. Phys. 79 (1981) 327 [INSPIRE].
J. Ambjørn, L. Chekhov, C.F. Kristjansen and Y. Makeenko, Matrix model calculations beyond the spherical limit, Nucl. Phys. B 404 (1993) 127 [Erratum ibid. 449 (1995) 681] [hep-th/9302014] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and Y.M. Makeenko, Multiloop correlators for two-dimensional quantum gravity, Phys. Lett. B 251 (1990) 517 [INSPIRE].
B. Eynard, T. Kimura and S. Ribault, Random matrices, arXiv:1510.04430 [INSPIRE].
B. Eynard, Large N expansion of the 2 matrix model, JHEP 01 (2003) 051 [hep-th/0210047] [INSPIRE].
M. Bertola, Free energy of the two matrix model/dToda tau function, Nucl. Phys. B 669 (2003) 435 [hep-th/0306184] [INSPIRE].
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: 2206.13531
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Eniceicu, D.S., Mahajan, R., Murdia, C. et al. Multi-instantons in minimal string theory and in matrix integrals. J. High Energ. Phys. 2022, 65 (2022). https://doi.org/10.1007/JHEP10(2022)065
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)065