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Late time behaviors of the expanding universe in the IIB matrix model

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Abstract

Recently we have studied the Lorentzian version of the IIB matrix model as a nonperturbative formulation of superstring theory. By Monte Carlo simulation, we have shown that the notion of time — as well as space — emerges dynamically from this model, and that we can uniquely extract the real-time dynamics, which turned out to be rather surprising: after some “critical time”, the SO(9) rotational symmetry of the ninedimensional space is spontaneously broken down to SO(3) and the three-dimensional space starts to expand rapidly. In this paper, we study the same model based on the classical equations of motion, which are expected to be valid at later times. After providing a general prescription to solve the equations, we examine a class of solutions, which correspond to manifestly commutative space. In particular, we find a solution with an expanding behavior that naturally solves the cosmological constant problem.

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References

  1. H. Liu, G.W. Moore and N. Seiberg, Strings in a time dependent orbifold, JHEP 06 (2002) 045 [hep-th/0204168] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. H. Liu, G.W. Moore and N. Seiberg, Strings in time dependent orbifolds, JHEP 10 (2002) 031 [hep-th/0206182] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Lawrence, On the instability of 3D null singularities, JHEP 11 (2002) 019 [hep-th/0205288] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G.T. Horowitz and J. Polchinski, Instability of space-like and null orbifold singularities, Phys. Rev. D 66 (2002) 103512 [hep-th/0206228] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. M. Berkooz, B. Craps, D. Kutasov and G. Rajesh, Comments on cosmological singularities in string theory, JHEP 03 (2003) 031 [hep-th/0212215] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. 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].

    MathSciNet  ADS  Google Scholar 

  7. 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].

    Article  MathSciNet  ADS  Google Scholar 

  8. R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. D.Z. Freedman, G.W. Gibbons and M. Schnabl, Matrix cosmology, AIP Conf. Proc. 743 (2005) 286 [hep-th/0411119] [INSPIRE].

    Article  ADS  Google Scholar 

  10. B. Craps, S. Sethi and E.P. Verlinde, A matrix big bang, JHEP 10 (2005) 005 [hep-th/0506180] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Li, A class of cosmological matrix models, Phys. Lett. B 626 (2005) 202 [hep-th/0506260] [INSPIRE].

    ADS  Google Scholar 

  12. S.R. Das and J. Michelson, PP wave big bangs: matrix strings and shrinking fuzzy spheres, Phys. Rev. D 72 (2005) 086005 [hep-th/0508068] [INSPIRE].

    ADS  Google Scholar 

  13. B. Chen, The time-dependent supersymmetric configurations in M-theory and matrix models, Phys. Lett. B 632 (2006) 393 [hep-th/0508191] [INSPIRE].

    ADS  Google Scholar 

  14. J.-H. She, A matrix model for Misner universe, JHEP 01 (2006) 002 [hep-th/0509067] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. E.J. Martinec, D. Robbins and S. Sethi, Toward the end of time, JHEP 08 (2006) 025 [hep-th/0603104] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. T. Ishino and N. Ohta, Matrix string description of cosmic singularities in a class of time-dependent solutions, Phys. Lett. B 638 (2006) 105 [hep-th/0603215] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. T. Matsuo, D. Tomino, W.-Y. Wen and S. Zeze, Quantum gravity equation in large-N Yang-Mills quantum mechanics, JHEP 11 (2008) 088 [arXiv:0807.1186] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. D. Klammer and H. Steinacker, Cosmological solutions of emergent noncommutative gravity, Phys. Rev. Lett. 102 (2009) 221301 [arXiv:0903.0986] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. J. Lee and H.S. Yang, Quantum gravity from noncommutative spacetime, SIGMA (2010) [arXiv:1004.0745] [INSPIRE].

  20. H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Space-time structures from IIB matrix model, Prog. Theor. Phys. 99 (1998) 713 [hep-th/9802085] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large-N reduced models, Nucl. Phys. B 545 (1999) 543 [hep-th/9811220] [INSPIRE].

    Article  ADS  Google Scholar 

  22. J. Ambjørn, K. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Large-N dynamics of dimensionally reduced 4D SU(N) super Yang-Mills theory, JHEP 07 (2000) 013 [hep-th/0003208] [INSPIRE].

    Article  ADS  Google Scholar 

  23. J. Ambjørn, K. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Monte Carlo studies of the IIB matrix model at large N, JHEP 07 (2000) 011 [hep-th/0005147] [INSPIRE].

    Article  ADS  Google Scholar 

  24. K. Anagnostopoulos and J. Nishimura, New approach to the complex action problem and its application to a nonperturbative study of superstring theory, Phys. Rev. D 66 (2002) 106008 [hep-th/0108041] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, A practical solution to the sign problem in a matrix model for dynamical compactification, JHEP 10 (2011) 126 [arXiv:1108.1534] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. J. Nishimura and G. Vernizzi, Spontaneous breakdown of Lorentz invariance in IIB matrix model, JHEP 04 (2000) 015 [hep-th/0003223] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. J. Nishimura and G. Vernizzi, Brane world from IIB matrices, Phys. Rev. Lett. 85 (2000) 4664 [hep-th/0007022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, JHEP 05 (2002) 001 [hep-th/0111102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. H. Kawai, S. Kawamoto, T. Kuroki, T. Matsuo and S. Shinohara, Mean field approximation of IIB matrix model and emergence of four-dimensional space-time, Nucl. Phys. B 647 (2002) 153 [hep-th/0204240] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. T. Aoyama and H. Kawai, Higher order terms of improved mean field approximation for IIB matrix model and emergence of four-dimensional space-time, Prog. Theor. Phys. 116 (2006) 405 [hep-th/0603146] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  31. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Quantum corrections on fuzzy sphere, Nucl. Phys. B 665 (2003) 520 [hep-th/0303120] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Effective actions of matrix models on homogeneous spaces, Nucl. Phys. B 679 (2004) 143 [hep-th/0307007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. T. Imai and Y. Takayama, Stability of fuzzy S 2 × S 2 geometry in IIB matrix model, Nucl. Phys. B 686 (2004) 248 [hep-th/0312241] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. J. Nishimura, T. Okubo and F. Sugino, Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings, JHEP 10 (2011) 135 [arXiv:1108.1293] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. W. Krauth, H. Nicolai and M. Staudacher, Monte Carlo approach to M-theory, Phys. Lett. B 431 (1998) 31 [hep-th/9803117] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  36. P. Austing and J.F. Wheater, Convergent Yang-Mills matrix theories, JHEP 04 (2001) 019 [hep-th/0103159] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding (3 + 1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9 + 1)-dimensions, Phys. Rev. Lett. 108 (2012) 011601 [arXiv:1108.1540] [INSPIRE].

    Article  ADS  Google Scholar 

  38. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory, Phys. Rev. D 86 (2012) 027901 [arXiv:1110.4803] [INSPIRE].

    ADS  Google Scholar 

  39. M. Fukuma, H. Kawai, Y. Kitazawa and A. Tsuchiya, String field theory from IIB matrix model, Nucl. Phys. B 510 (1998) 158 [hep-th/9705128] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  40. J. Ambjørn, J. Jurkiewicz and R. Loll, Reconstructing the universe, Phys. Rev. D 72 (2005) 064014 [hep-th/0505154] [INSPIRE].

    ADS  Google Scholar 

  41. H. Kawai and T. Okada, Asymptotically vanishing cosmological constant in the multiverse, Int. J. Mod. Phys. A 26 (2011) 3107 [arXiv:1104.1764] [INSPIRE].

    ADS  Google Scholar 

  42. H. Steinacker, Split noncommutativity and compactified brane solutions in matrix models, Prog. Theor. Phys. 126 (2011) 613 [arXiv:1106.6153] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  43. A. Chatzistavrakidis, On Lie-algebraic solutions of the type IIB matrix model, Phys. Rev. D 84 (2011) 106010 [arXiv:1108.1107] [INSPIRE].

    ADS  Google Scholar 

  44. J. Patera, R. Sharp, P. Winternitz and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys. 17 (1976) 986 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. J. Madore, The fuzzy sphere, Class. Quant. Grav. 9 (1992) 69 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. S. Iso, Y. Kimura, K. Tanaka and K. Wakatsuki, Noncommutative gauge theory on fuzzy sphere from matrix model, Nucl. Phys. B 604 (2001) 121 [hep-th/0101102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. J. Nishimura, The origin of space-time as seen from matrix model simulations, Prog. Theor. Exp. Phys. 2012 (2012) 01A101 [arXiv:1205.6870] [INSPIRE].

    Google Scholar 

  48. H. Steinacker, Emergent geometry and gravity from matrix models: an introduction, Class. Quant. Grav. 27 (2010) 133001 [arXiv:1003.4134] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. M. Hanada, H. Kawai and Y. Kimura, Describing curved spaces by matrices, Prog. Theor. Phys. 114 (2006) 1295 [hep-th/0508211] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. A. Chatzistavrakidis, H. Steinacker and G. Zoupanos, Intersecting branes and a standard model realization in matrix models, JHEP 09 (2011) 115 [arXiv:1107.0265] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. H. Aoki, Chiral fermions and the standard model from the matrix model compactified on a torus, Prog. Theor. Phys. 125 (2011) 521 [arXiv:1011.1015] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  52. N. Ja. Vilenkin and A.U. Klimyk, Representation of Lie groups and special functions volume 1, Kluwer Academic Publishers, Dordrecht The Netherlands (1991).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Sang-Woo Kim

  2. Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

  3. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

  4. Department of Physics, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Asato Tsuchiya

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  1. Sang-Woo Kim
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  2. Jun Nishimura
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Correspondence to Asato Tsuchiya.

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ArXiv ePrint: 1208.0711

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Kim, SW., Nishimura, J. & Tsuchiya, A. Late time behaviors of the expanding universe in the IIB matrix model. J. High Energ. Phys. 2012, 147 (2012). https://doi.org/10.1007/JHEP10(2012)147

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