Abstract
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.
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References
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].
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].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].
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].
N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
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].
D. Kutasov and N. Seiberg, Noncritical superstrings, Phys. Lett. B 251 (1990) 67 [INSPIRE].
D. Kutasov, Some properties of (non)critical strings, hep-th/9110041 [INSPIRE].
S. Murthy, Notes on noncritical superstrings in various dimensions, JHEP 11 (2003) 056 [hep-th/0305197] [INSPIRE].
H. Ita, H. Nieder and Y. Oz, On type-II strings in two dimensions, JHEP 06 (2005) 055 [hep-th/0502187] [INSPIRE].
P.A. Grassi and Y. Oz, Non-critical covariant superstrings, hep-th/0507168 [INSPIRE].
T. Takayanagi, Comments on 2-D type IIA string and matrix model, JHEP 11 (2004) 030 [hep-th/0408086] [INSPIRE].
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].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
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].
A. Gupta, S.P. Trivedi and M.B. Wise, Random Surfaces in Conformal Gauge, Nucl. Phys. B 340 (1990) 475 [INSPIRE].
M. Goulian and M. Li, Correlation functions in Liouville theory, Phys. Rev. Lett. 66 (1991) 2051 [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].
I.R. Klebanov, String theory in two-dimensions, hep-th/9108019 [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. Volume 3, M. Shifman et al. eds., pg. 1758-1827, [hep-th/0307195] [INSPIRE].
S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287 [INSPIRE].
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].
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].
K. Becker, G.-Y. Guo and D. Robbins, Disc amplitudes, picture changing and space-time actions, JHEP 01 (2012) 127 [arXiv:1106.3307] [INSPIRE].
J.J. Atick, J.M. Rabin and A. Sen, An Ambiguity in Fermionic String Perturbation Theory, Nucl. Phys. B 299 (1988) 279 [INSPIRE].
C. Imbimbo and S. Mukhi, The topological matrix model of c = 1 string, Nucl. Phys. B 449 (1995) 553 [hep-th/9505127] [INSPIRE].
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].
K. Itoh and N. Ohta, Spectrum of two-dimensional (super)gravity, Prog. Theor. Phys. Suppl. 110 (1992) 97 [hep-th/9201034] [INSPIRE].
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].
J. McGreevy and H.L. Verlinde, Strings from tachyons: The c = 1 matrix reloaded, JHEP 12 (2003) 054 [hep-th/0304224] [INSPIRE].
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].
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].
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].
T. Fukuda and K. Hosomichi, Three point functions in sine-Liouville theory, JHEP 09 (2001) 003 [hep-th/0105217] [INSPIRE].
H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
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Kuroki, T., Sugino, F. Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background. J. High Energ. Phys. 2014, 6 (2014). https://doi.org/10.1007/JHEP03(2014)006
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DOI: https://doi.org/10.1007/JHEP03(2014)006