Abstract
In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) R6041 [hep-th/9407031] [INSPIRE].
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
M. Billó, M. Frau, I. Pesando, F. Fucito, A. Lerda and A. Liccardo, Classical gauge instantons from open strings, JHEP 02 (2003) 045 [hep-th/0211250] [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].
S.R. Das and A. Jevicki, String field theory and physical interpretation of D = 1 strings, Mod. Phys. Lett. A 5 (1990) 1639 [INSPIRE].
A.M. Sengupta and S.R. Wadia, Excitations and interactions in d = 1 string theory, Int. J. Mod. Phys. A 6 (1991) 1961 [INSPIRE].
D.J. Gross and I.R. Klebanov, Fermionic string field theory of c = 1 two-dimensional quantum gravity, Nucl. Phys. B 352 (1991) 671 [INSPIRE].
I.R. Klebanov, String theory in two-dimensions, in Spring school on string theory and quantum gravity (to be followed by workshop), (1991) [hep-th/9108019] [INSPIRE].
G.W. Moore, M.R. Plesser and S. Ramgoolam, Exact S matrix for 2D string theory, Nucl. Phys. B 377 (1992) 143 [hep-th/9111035] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, Multi-instanton calculus in c = 1 string theory, arXiv:1912.07170 [INSPIRE].
C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed superstring field theory and its applications, Int. J. Mod. Phys. A 32 (2017) 1730021 [arXiv:1703.06410] [INSPIRE].
A. Sen, String field theory as world-sheet UV regulator, JHEP 10 (2019) 119 [arXiv:1902.00263] [INSPIRE].
P.V. Larocca and C. Maccaferri, BCFT and OSFT moduli: an exact perturbative comparison, Eur. Phys. J. C 77 (2017) 806 [arXiv:1702.06489] [INSPIRE].
A. Sen, Fixing an ambiguity in two dimensional string theory using string field theory, JHEP 03 (2020) 005 [arXiv:1908.02782] [INSPIRE].
A. Sen, D-instanton perturbation theory, JHEP 08 (2020) 075 [arXiv:2002.04043] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, private communication.
A. Sen, Divergent ⇒ complex amplitudes in two dimensional string theory, JHEP 02 (2021) 086 [arXiv:2003.12076] [INSPIRE].
H. Hata and B. Zwiebach, Developing the covariant Batalin-Vilkovisky approach to string theory, Annals Phys. 229 (1994) 177 [hep-th/9301097] [INSPIRE].
B. Zwiebach, Quantum open string theory with manifest closed string factorization, Phys. Lett. B 256 (1991) 22 [INSPIRE].
B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241] [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Gauge algebra and quantization, Phys. Lett. B 102 (1981) 27 [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. 30 (1984) 508] [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton, NJ, U.S.A. (1992).
A. Sen and B. Zwiebach, A note on gauge transformations in Batalin-Vilkovisky theory, Phys. Lett. B 320 (1994) 29 [hep-th/9309027] [INSPIRE].
H. Kajiura, Homotopy algebra morphism and geometry of classical string field theory, Nucl. Phys. B 630 (2002) 361 [hep-th/0112228] [INSPIRE].
H. Kajiura, Noncommutative homotopy algebras associated with open strings, Rev. Math. Phys. 19 (2007) 1 [math.QA/0306332] [INSPIRE].
H. Erbin, C. Maccaferri, M. Schnabl and J. Vošmera, Classical algebraic structures in string theory effective actions, JHEP 11 (2020) 123 [arXiv:2006.16270] [INSPIRE].
T. Erler and H. Matsunaga, Mapping between Witten and Lightcone string field theories, arXiv:2012.09521 [INSPIRE].
A. Sen, Wilsonian effective action of superstring theory, JHEP 01 (2017) 108 [arXiv:1609.00459] [INSPIRE].
H. Erbin, C. Maccaferri and J. Vošmera, Localization of effective actions in heterotic string field theory, JHEP 02 (2020) 059 [arXiv:1912.05463] [INSPIRE].
N. Nakanishi, Covariant quantization of the electromagnetic field in the Landau gauge, Prog. Theor. Phys. 35 (1966) 1111 [INSPIRE].
B. Lautrup, Canonical quantum electrodynamics in covariant gauges, Kgl. Dan. Vid. Se. Mat. Fys. Medd. 35 (11) (1967) 1.
E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic geometry of superstring perturbation theory, arXiv:1703.10563 [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic geometry and closed bosonic string field theory. Part I. The string vertices via hyperbolic Riemann surfaces, JHEP 08 (2019) 157 [arXiv:1706.07366] [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic geometry and closed bosonic string field theory. Part II. The rules for evaluating the quantum BV master action, JHEP 08 (2019) 177 [arXiv:1708.04977] [INSPIRE].
K. Costello and B. Zwiebach, Hyperbolic string vertices, arXiv:1909.00033 [INSPIRE].
M. Cho, Open-closed hyperbolic string vertices, JHEP 05 (2020) 046 [arXiv:1912.00030] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, One loop tadpole in heterotic string field theory, JHEP 11 (2017) 056 [arXiv:1704.01210] [INSPIRE].
A. Sen, Cutkosky rules and unitarity (violation) in D-instanton amplitudes, arXiv:2012.00041 [INSPIRE].
D. Ghoshal and A. Sen, Gauge and general coordinate invariance in nonpolynomial closed string theory, Nucl. Phys. B 380 (1992) 103 [hep-th/9110038] [INSPIRE].
E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
A. Sen, Gauge invariant 1PI effective action for superstring field theory, JHEP 06 (2015) 022 [arXiv:1411.7478] [INSPIRE].
M.B. Green and P. Vanhove, D instantons, strings and M-theory, Phys. Lett. B 408 (1997) 122 [hep-th/9704145] [INSPIRE].
M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].
E. Kiritsis and B. Pioline, On R4 threshold corrections in IIB string theory and (p, q) string instantons, Nucl. Phys. B 508 (1997) 509 [hep-th/9707018] [INSPIRE].
B. Pioline and E. Kiritsis, U duality and D-brane combinatorics, Phys. Lett. B 418 (1998) 61 [hep-th/9710078] [INSPIRE].
N.A. Obers and B. Pioline, Eisenstein series and string thresholds, Commun. Math. Phys. 209 (2000) 275 [hep-th/9903113] [INSPIRE].
M.B. Green, H.-H. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].
M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].
A. Basu, The D4 R4 term in type IIB string theory on T2 and U-duality, Phys. Rev. D 77 (2008) 106003 [arXiv:0708.2950] [INSPIRE].
A. Basu, The D6 R4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106004 [arXiv:0712.1252] [INSPIRE].
B. Pioline, R4 couplings and automorphic unipotent representations, JHEP 03 (2010) 116 [arXiv:1001.3647] [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81 (2010) 086008 [arXiv:1001.2535] [INSPIRE].
M.B. Green, S.D. Miller, J.G. Russo and P. Vanhove, Eisenstein series for higher-rank groups and string theory amplitudes, Commun. Num. Theor. Phys. 4 (2010) 551 [arXiv:1004.0163] [INSPIRE].
M.B. Green, S.D. Miller and P. Vanhove, Small representations, string instantons, and Fourier modes of Eisenstein series, J. Number Theor. 146 (2015) 187 [arXiv:1111.2983] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional form of D = 11 supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
M.B. Green, S.D. Miller and P. Vanhove, SL(2, Z )-invariance and D-instanton contributions to the D6 R4 interaction, Commun. Num. Theor. Phys. 09 (2015) 307 [arXiv:1404.2192] [INSPIRE].
B. Pioline, D6 R4 amplitudes in various dimensions, JHEP 04 (2015) 057 [arXiv:1502.03377] [INSPIRE].
G. Bossard and A. Kleinschmidt, Loops in exceptional field theory, JHEP 01 (2016) 164 [arXiv:1510.07859] [INSPIRE].
G. Bossard and A. Kleinschmidt, Cancellation of divergences up to three loops in exceptional field theory, JHEP 03 (2018) 100 [arXiv:1712.02793] [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, I.R. Klebanov, D. Kutasov, J.M. Maldacena, E.J. Martinec and N. Seiberg, A new hat for the c = 1 matrix model, in From fields to strings: circumnavigating theoretical physics. A conference in tribute to Ian Kogan, (2003), pg. 1758 [hep-th/0307195] [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].
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: 2012.11624
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
Sen, A. D-instantons, string field theory and two dimensional string theory. J. High Energ. Phys. 2021, 61 (2021). https://doi.org/10.1007/JHEP11(2021)061
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)061