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Prog. Theor. Phys. Vol. 116 No. 2 (2006) pp. 405-415

Higher Order Terms in the Improved Mean Field Approximation for the IIB Matrix Model and the Emergence of Four-Dimensional Space-Time

Tatsumi Aoyama¹ and Hikaru Kawai^1,2

¹Theoretical Physics Laboratory, RIKEN, Wako 351-0198, Japan
²Department of Physics, Kyoto University, Kyoto 606-8502, Japan

(Received May 31, 2006)

Abstract:

The spontaneous breakdown of SO(10) symmetry in the IIB matrix model has been studied using the improved mean field approximation (IMFA). In this report, the eighth-order contribution to the improved perturbative series is obtained, which involves the evaluation of 20410 planar two-particle irreducible vacuum diagrams. We consider SO(d)-preserving configurations as an ansatz (d = 4,7). The development of a plateau, representing the condition of self-consistency, is seen in both ansatz. A large ratio of the space-time extent of the d-dimensional part to that of the remaining (10-d)-dimensional part is obtained for the SO(4) ansatz evaluated at representative points of the plateau. This is interpreted as the emergence of four-dimensional space-time in the IIB matrix model.

URL : http://ptp.ipap.jp/link?PTP/116/405/
DOI : 10.1143/PTP.116.405

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References:

1. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, Nucl. Phys. B 498 (1997), 467[CrossRef].
2. H. Aoki, S. Iso, H. Kawai, Y. Kitazawa, A. Tsuchiya and T. Tada, Prog. Theor. Phys. Suppl. No. 134 (1999), 47[PTP].
3. T. Hotta, J. Nishimura and A. Tsuchiya, Nucl. Phys. B 545 (1999), 543[CrossRef].
   J. Ambjørn, J. Nishimura, K. N. Anagnostopoulos, W. Bietenholz and T. Hotta, J. High Energy Phys. 07 (2000), 011[CrossRef].
   J. Ambjørn, K. N. Anagnostopoulos, W. Bietenholz, F. Hofheinz and J. Nishimura, Phys. Rev. D 65 (2002), 086001[APS].
   J. Nishimura and G. Vernizzi, Phys. Rev. Lett. 85 (2000), 4664[APS]; J. High Energy Phys. 04 (2000), 015[CrossRef].
   J. Nishimura, Phys. Rev. D 65 (2002), 105012[APS].
4. K. N. Anagnostopoulos and J. Nishimura, Phys. Rev. D 66 (2002), 106008[APS].
   J. Ambjørn, K. N. Anagnostopoulos, J. Nishimura and J. J. M. Verbaarschot, J. High Energy Phys. 10 (2002), 062[CrossRef].
5. D. Kabat and G. Lifschytz, Nucl. Phys. B 571 (2000), 419[CrossRef].
   S. Oda and F. Sugino, J. High Energy Phys. 03 (2001), 026[CrossRef].
   F. Sugino, J. High Energy Phys. 07 (2001), 014[CrossRef].
6. J. Nishimura and F. Sugino, J. High Energy Phys. 05 (2002), 001[CrossRef].
7. J. Nishimura, T. Okubo and F. Sugino, Prog. Theor. Phys. 114 (2005), 487[PTP].
8. H. Kawai, S. Kawamoto, T. Kuroki, T. Matsuo and S. Shinohara, Nucl. Phys. B 647 (2002), 153[CrossRef].
9. H. Kawai, S. Kawamoto, T. Kuroki and S. Shinohara, Prog. Theor. Phys. 109 (2003), 115[PTP].
10. P. M. Stevenson, Phys. Rev. D 23 (1981), 2916[APS].
    A. Dhar, Phys. Lett. B 128 (1983), 407[CrossRef].
11. T. Aoyama, T. Matsuo and Y. Shibusa, Prog. Theor. Phys. 115 (2006), 473[PTP].
12. J. Nishimura, T. Okubo and F. Sugino, J. High Energy Phys. 10 (2002), 043[CrossRef]; ibid. 10 (2003), 057[CrossRef].
13. R. Fukuda, M. Komachiya, S. Yokojima, Y. Suzuki, K. Okumura and T. Inagaki, Prog. Theor. Phys. Suppl. No. 121 (1995), 1[PTP].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 119 No. 2 (2008) pp. 303-321 :

   Improved Renormalization Group Analysis for Yang-Mills Theory

   Shoichi Kawamoto and Toshihiro Matsuo

2. Progress of Theoretical Physics Vol. 125 No. 3 (2011) pp. 537-563 :

   Spontaneous Breaking of the Rotational Symmetry in Dimensionally Reduced Super Yang-Mills Models

   Tatsumi Aoyama, Jun Nishimura and Toshiyuki Okubo

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