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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Morozov: arXiv:hep-th/0502010
J.J.M. Verbaarschot: arXiv:hep-th/0502029
T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong: Rev. Mod. Phys. 53, 385 (1981)
T. Guhr, A. Muller-Groeling, H.A. Weidenmuller: Phys. Rep. 299, 189 (1998) [arXiv:cond-mat/9707301]
J.C. Osborn, D. Toublan, J.J.M. Verbaarschot: Nucl. Phys. B 540, 317 (1999) [arXiv:hep-th/9806110]
J.J.M. Verbaarschot: Phys. Rev. Lett. 72, 2531 (1994) [arXiv:hep-th/9401059]
E.V. Shuryak, J.J.M. Verbaarschot: Nucl. Phys. A 560, 306 (1993) [arXiv:hep- th/9212088]
N. Ishibashi, H. Kawai, Y. Kitazawa, A. Tsuchiya: Nucl. Phys. B 498, 467 (1997) [arXiv:hep-th/9612115]
T. Banks, W. Fischler, S.H. Shenker, L. Susskind: Phys. Rev. D 55, 5112 (1997) [arXiv:hep-th/9610043]
J. Polchinski: Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, Y. Oz: Phys. Rep. 323, 183 (2000) [arXiv:hep-th/9905111]
J. Polchinski, String Theory, 2 volumes, (Cambridge University Press, Cambridge, 1998)
E. Kiritsis: arXiv:hep-th/9709062
T. Eguchi, H. Kawai: Phys. Rev. Lett. 48, 1063 (1982)
D. Berenstein, J.M. Maldacena, H. Nastase: JHEP 0204, 013 (2002) [arXiv:hep-th/0202021]
D. Berenstein, E. Gava, J.M. Maldacena, K.S. Narain, H. Nastase: arXiv:hep-th/0203249
D. Berenstein, H. Nastase: arXiv:hep-th/0205048
P. Valtancoli: Int. J. Mod. Phys. A 18, 967 (2003) [arXiv:hep-th/0206075]
C. Sochichiu: Phys. Lett. B 574, 105 (2003) [arXiv:hep-th/0206239]
Y.K. Cheung, M. Krogh: Nucl. Phys. B 528, 185 (1998) [arXiv:hep-th/9803031]
C.S. Chu, P.M. Ho: Nucl. Phys. B 550, 151 (1999) [arXiv:hep-th/9812219]
C.S. Chu, P.M. Ho: Nucl. Phys. B 568, 447 (2000) [arXiv:hep-th/9906192]
N. Seiberg, E. Witten: JHEP 9909, 032 (1999) [arXiv:hep-th/9908142]
C. Sochichiu: JHEP 0005, 026 (2000) [arXiv:hep-th/0004062]
C. Sochichiu: Phys. Lett. B 485, 202 (2000) [arXiv:hep-th/0005156]
C. Sochichiu: JHEP 0008, 048 (2000) [arXiv:hep-th/0007127]
C. Sochichiu: arXiv:hep-th/0010149
C. Sochichiu: arXiv:hep-th/0012262
E. Kiritsis, C. Sochichiu: arXiv:hep-th/0202065
C. Sochichiu: arXiv:hep-th/0202014
J.A. Harvey: arXiv:hep-th/0102076
S. Minwalla, M. Van Raamsdonk, N. Seiberg: JHEP 0002, 020 (2000) [arXiv:hep-th/9912072]
M. Van Raamsdonk, N. Seiberg: JHEP 0003, 035 (2000) [arXiv:hep-th/0002186]
S. Sarkar: JHEP 0206, 003 (2002) [arXiv:hep-th/0202171]
W. Bietenholz, F. Hofheinz, J. Nishimura: JHEP 0209, 009 (2002) [arXiv:hep-th/0203151]
A.A. Slavnov: Phys. Lett. B 565, 246 (2003) [arXiv:hep-th/0304141]
M. Buric, V. Radovanovic: arXiv:hep-th/0305236
M.M. Sheikh-Jabbari: JHEP 9906, 015 (1999) [arXiv:hep-th/9903107]
H.B. Nielsen, M. Ninomiya: Phys. Lett. B 105, 219 (1981)
N. Kitsunezaki, J. Nishimura: Nucl. Phys. B 526, 351 (1998) [arXiv:hep-th/9707162]
A.P. Balachandran, G. Immirzi: Phys. Rev. D 68, 065023 (2003) [arXiv:hep-th/0301242]
V.P. Nair, A.P. Polychronakos: Phys. Rev. Lett. 87, 030403 (2001) [arXiv:hep-th/0102181]
D. Bak, K.M. Lee, J.H. Park, “Comments on noncommutative gauge theories”, Phys. Lett. B 501, 305–312 (2001) [arXiv:hep-th/0011244]
T. Ishikawa, S.I. Kuroki, A. Sako: J. Math. Phys. 43, 872 (2002) [arXiv:hep-th/0107033]
A. Agarwal, S.G. Rajeev: Mod. Phys. Lett. A 19, 2549 (2004) [arXiv:hep-th/0405116]
S. Bellucci, C. Sochichiu: Nucl. Phys. B 726, 233 (2005) [arXiv:hep-th/0410010]
R. Dijkgraaf, C. Vafa: arXiv:hep-th/0208048
R. Dijkgraaf, C. Vafa: Nucl. Phys. B 644, 21 (2002) [arXiv:hep-th/0207106]
R. Dijkgraaf, C. Vafa: Nucl. Phys. B 644, 3 (2002) [arXiv:hep-th/0206255]
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/3-540-33314-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33313-5
Online ISBN: 978-3-540-33314-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)