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Part of the book series: Lecture Notes in Physics ((LNP,volume 698))

Abstract

Matrix models and their connections to string theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. The most interesting are IKKT and BFSS models. They are introduced as 0+0 and 1+0-dimensional reduction of Yang–Mills model respectively. They are obtained via the deformations of string/membrane worldsheet/worldvolume. Classical solutions leading to noncommutative gauge models are considered.

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References

  1. A. Morozov: arXiv:hep-th/0502010

    Google Scholar 

  2. J.J.M. Verbaarschot: arXiv:hep-th/0502029

    Google Scholar 

  3. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong: Rev. Mod. Phys. 53, 385 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  4. T. Guhr, A. Muller-Groeling, H.A. Weidenmuller: Phys. Rep. 299, 189 (1998) [arXiv:cond-mat/9707301]

    Article  MathSciNet  ADS  Google Scholar 

  5. J.C. Osborn, D. Toublan, J.J.M. Verbaarschot: Nucl. Phys. B 540, 317 (1999) [arXiv:hep-th/9806110]

    Article  MathSciNet  ADS  Google Scholar 

  6. J.J.M. Verbaarschot: Phys. Rev. Lett. 72, 2531 (1994) [arXiv:hep-th/9401059]

    Article  MathSciNet  ADS  Google Scholar 

  7. E.V. Shuryak, J.J.M. Verbaarschot: Nucl. Phys. A 560, 306 (1993) [arXiv:hep- th/9212088]

    Article  ADS  Google Scholar 

  8. N. Ishibashi, H. Kawai, Y. Kitazawa, A. Tsuchiya: Nucl. Phys. B 498, 467 (1997) [arXiv:hep-th/9612115]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. T. Banks, W. Fischler, S.H. Shenker, L. Susskind: Phys. Rev. D 55, 5112 (1997) [arXiv:hep-th/9610043]

    Article  MathSciNet  ADS  Google Scholar 

  10. J. Polchinski: Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, Y. Oz: Phys. Rep. 323, 183 (2000) [arXiv:hep-th/9905111]

    Article  MathSciNet  ADS  Google Scholar 

  12. J. Polchinski, String Theory, 2 volumes, (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  13. E. Kiritsis: arXiv:hep-th/9709062

    Google Scholar 

  14. T. Eguchi, H. Kawai: Phys. Rev. Lett. 48, 1063 (1982)

    Article  ADS  Google Scholar 

  15. D. Berenstein, J.M. Maldacena, H. Nastase: JHEP 0204, 013 (2002) [arXiv:hep-th/0202021]

    Article  MathSciNet  ADS  Google Scholar 

  16. D. Berenstein, E. Gava, J.M. Maldacena, K.S. Narain, H. Nastase: arXiv:hep-th/0203249

    Google Scholar 

  17. D. Berenstein, H. Nastase: arXiv:hep-th/0205048

    Google Scholar 

  18. P. Valtancoli: Int. J. Mod. Phys. A 18, 967 (2003) [arXiv:hep-th/0206075]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. C. Sochichiu: Phys. Lett. B 574, 105 (2003) [arXiv:hep-th/0206239]

    MATH  MathSciNet  ADS  Google Scholar 

  20. Y.K. Cheung, M. Krogh: Nucl. Phys. B 528, 185 (1998) [arXiv:hep-th/9803031]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. C.S. Chu, P.M. Ho: Nucl. Phys. B 550, 151 (1999) [arXiv:hep-th/9812219]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. C.S. Chu, P.M. Ho: Nucl. Phys. B 568, 447 (2000) [arXiv:hep-th/9906192]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. N. Seiberg, E. Witten: JHEP 9909, 032 (1999) [arXiv:hep-th/9908142]

    Article  MathSciNet  ADS  Google Scholar 

  24. C. Sochichiu: JHEP 0005, 026 (2000) [arXiv:hep-th/0004062]

    ADS  Google Scholar 

  25. C. Sochichiu: Phys. Lett. B 485, 202 (2000) [arXiv:hep-th/0005156]

    Article  MathSciNet  ADS  Google Scholar 

  26. C. Sochichiu: JHEP 0008, 048 (2000) [arXiv:hep-th/0007127]

    Article  MathSciNet  ADS  Google Scholar 

  27. C. Sochichiu: arXiv:hep-th/0010149

    Google Scholar 

  28. C. Sochichiu: arXiv:hep-th/0012262

    Google Scholar 

  29. E. Kiritsis, C. Sochichiu: arXiv:hep-th/0202065

    Google Scholar 

  30. C. Sochichiu: arXiv:hep-th/0202014

    Google Scholar 

  31. J.A. Harvey: arXiv:hep-th/0102076

    Google Scholar 

  32. S. Minwalla, M. Van Raamsdonk, N. Seiberg: JHEP 0002, 020 (2000) [arXiv:hep-th/9912072]

    Article  ADS  Google Scholar 

  33. M. Van Raamsdonk, N. Seiberg: JHEP 0003, 035 (2000) [arXiv:hep-th/0002186]

    Article  Google Scholar 

  34. S. Sarkar: JHEP 0206, 003 (2002) [arXiv:hep-th/0202171]

    Article  MathSciNet  ADS  Google Scholar 

  35. W. Bietenholz, F. Hofheinz, J. Nishimura: JHEP 0209, 009 (2002) [arXiv:hep-th/0203151]

    Google Scholar 

  36. A.A. Slavnov: Phys. Lett. B 565, 246 (2003) [arXiv:hep-th/0304141]

    MATH  MathSciNet  ADS  Google Scholar 

  37. M. Buric, V. Radovanovic: arXiv:hep-th/0305236

    Google Scholar 

  38. M.M. Sheikh-Jabbari: JHEP 9906, 015 (1999) [arXiv:hep-th/9903107]

    Google Scholar 

  39. H.B. Nielsen, M. Ninomiya: Phys. Lett. B 105, 219 (1981)

    ADS  Google Scholar 

  40. N. Kitsunezaki, J. Nishimura: Nucl. Phys. B 526, 351 (1998) [arXiv:hep-th/9707162]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. A.P. Balachandran, G. Immirzi: Phys. Rev. D 68, 065023 (2003) [arXiv:hep-th/0301242]

    Article  MathSciNet  ADS  Google Scholar 

  42. V.P. Nair, A.P. Polychronakos: Phys. Rev. Lett. 87, 030403 (2001) [arXiv:hep-th/0102181]

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Bak, K.M. Lee, J.H. Park, “Comments on noncommutative gauge theories”, Phys. Lett. B 501, 305–312 (2001) [arXiv:hep-th/0011244]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  44. T. Ishikawa, S.I. Kuroki, A. Sako: J. Math. Phys. 43, 872 (2002) [arXiv:hep-th/0107033]

    MATH  Google Scholar 

  45. A. Agarwal, S.G. Rajeev: Mod. Phys. Lett. A 19, 2549 (2004) [arXiv:hep-th/0405116]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. S. Bellucci, C. Sochichiu: Nucl. Phys. B 726, 233 (2005) [arXiv:hep-th/0410010]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. R. Dijkgraaf, C. Vafa: arXiv:hep-th/0208048

    Google Scholar 

  48. R. Dijkgraaf, C. Vafa: Nucl. Phys. B 644, 21 (2002) [arXiv:hep-th/0207106]

    Article  MATH  MathSciNet  ADS  Google Scholar 

  49. R. Dijkgraaf, C. Vafa: Nucl. Phys. B 644, 3 (2002) [arXiv:hep-th/0206255]

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Sochichiu, C. (2006). Matrix Models. In: Bellucci, S. (eds) Supersymmetric Mechanics – Vol. 1. Lecture Notes in Physics, vol 698. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33314-2_5

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