Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background

  • Tsunehide Kuroki
  • Fumihiko Sugino
Open Access


In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.


Matrix Models 2D Gravity Superstrings and Heterotic Strings 


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.


  1. [1]
    T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: A conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].ADSMathSciNetGoogle Scholar
  2. [2]
    N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    T. Kuroki and F. Sugino, New critical behavior in a supersymmetric double-well matrix model, Nucl. Phys. B 867 (2013) 448 [arXiv:1208.3263] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    T. Kuroki and F. Sugino, Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping, Nucl. Phys. B 844 (2011) 409 [arXiv:1009.6097] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    D. Kutasov and N. Seiberg, Noncritical superstrings, Phys. Lett. B 251 (1990) 67 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    D. Kutasov, Some properties of (non)critical strings, hep-th/9110041 [INSPIRE].
  10. [10]
    S. Murthy, Notes on noncritical superstrings in various dimensions, JHEP 11 (2003) 056 [hep-th/0305197] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    H. Ita, H. Nieder and Y. Oz, On type-II strings in two dimensions, JHEP 06 (2005) 055 [hep-th/0502187] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    P.A. Grassi and Y. Oz, Non-critical covariant superstrings, hep-th/0507168 [INSPIRE].
  13. [13]
    T. Takayanagi, Comments on 2-D type IIA string and matrix model, JHEP 11 (2004) 030 [hep-th/0408086] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    A. Jevicki and T. Yoneya, A deformed matrix model and the black hole background in two-dimensional string theory, Nucl. Phys. B 411 (1994) 64 [hep-th/9305109] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  15. [15]
    E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    H. Ooguri, Y. Oz and Z. Yin, D-branes on Calabi-Yau spaces and their mirrors, Nucl. Phys. B 477 (1996) 407 [hep-th/9606112] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    A. Gupta, S.P. Trivedi and M.B. Wise, Random Surfaces in Conformal Gauge, Nucl. Phys. B 340 (1990) 475 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    M. Goulian and M. Li, Correlation functions in Liouville theory, Phys. Rev. Lett. 66 (1991) 2051 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    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].ADSCrossRefGoogle Scholar
  20. [20]
    I.R. Klebanov, String theory in two-dimensions, hep-th/9108019 [INSPIRE].
  21. [21]
    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. Volume 3, M. Shifman et al. eds., pg. 1758-1827, [hep-th/0307195] [INSPIRE].
  22. [22]
    S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287 [INSPIRE].
  23. [23]
    M. Bershadsky and I.R. Klebanov, Partition functions and physical states in two-dimensional quantum gravity and supergravity, Nucl. Phys. B 360 (1991) 559 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    C.G. Callan Jr., C. Lovelace, C. Nappi and S. Yost, Loop Corrections to Superstring Equations of Motion, Nucl. Phys. B 308 (1988) 221 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    K. Becker, G.-Y. Guo and D. Robbins, Disc amplitudes, picture changing and space-time actions, JHEP 01 (2012) 127 [arXiv:1106.3307] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    J.J. Atick, J.M. Rabin and A. Sen, An Ambiguity in Fermionic String Perturbation Theory, Nucl. Phys. B 299 (1988) 279 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    C. Imbimbo and S. Mukhi, The topological matrix model of c = 1 string, Nucl. Phys. B 449 (1995) 553 [hep-th/9505127] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    K. Itoh and N. Ohta, BRST Cohomology and Physical States in 2D Supergravity Coupled to ĉ ≤ 1 Matter,Nucl. Phys. B 377 (1992) 113 [hep-th/9110013] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  29. [29]
    K. Itoh and N. Ohta, Spectrum of two-dimensional (super)gravity, Prog. Theor. Phys. Suppl. 110 (1992) 97 [hep-th/9201034] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  30. [30]
    P. Bouwknegt, J.G. McCarthy and K. Pilch, Ground ring for the 2-D NSR string, Nucl. Phys. B 377 (1992) 541 [hep-th/9112036] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  31. [31]
    J. McGreevy and H.L. Verlinde, Strings from tachyons: The c = 1 matrix reloaded, JHEP 12 (2003) 054 [hep-th/0304224] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    I.R. Klebanov, J.M. Maldacena and N. Seiberg, D-brane decay in two-dimensional string theory, JHEP 07 (2003) 045 [hep-th/0305159] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    J. McGreevy, J. Teschner and H.L. Verlinde, Classical and quantum D-branes in 2 − D string theory, JHEP 01 (2004) 039 [hep-th/0305194] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    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].ADSCrossRefMathSciNetGoogle Scholar
  35. [35]
    T. Fukuda and K. Hosomichi, Three point functions in sine-Liouville theory, JHEP 09 (2001) 003 [hep-th/0105217] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  36. [36]
    H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Kobayashi-Maskawa Institute for the Origin of Particles and the UniverseNagoya UniversityNagoyaJapan
  2. 2.Okayama Institute for Quantum PhysicsOkayamaJapan

Personalised recommendations