The large-N reduction in matrix quantum mechanics - A bridge between BFSS and IKKT -

Journal of High Energy Physics

Volumn , Issue 9, 2005, Pages 1031-1042

  Kawahara, Naoyuki ^a,b   Nishimura, Jun ^a,c  

^a HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

^c GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

Author keywords

Matrix Models; Nonperturbative Effects

Indexed keywords

EID: 26044441120     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2005/09/040     Document Type: Article

References (66)

1. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory 1982 Phys. Rev. Lett. 48 1063
2. R. Dijkgraaf and C. Vafa, A perturbative window into non-perturbative physics [hep-th/0208048]
3. H. Kawai, T. Kuroki and T. Morita, Dijkgraaf-Vafa theory as large-N reduction 2003 Nucl. Phys. B 664 185 [hep-th/0303210]
4. D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a spatial lattice 2003 J. High Energy Phys. JHEP05(2003)037 [hep-lat/0206019]
5. A.G. Cohen, D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a euclidean spacetime lattice. I: a target theory with four supercharges 2003 J. High Energy Phys. JHEP08(2003)024 [hep-lat/0302017]
6. A.G. Cohen, D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a euclidean spacetime lattice. II: target theories with eight supercharges 2003 J. High Energy Phys. JHEP12(2003)031 [hep-lat/0307012]
7. D.B. Kaplan and M. Unsal, A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges [hep-lat/0503039]
8. S. Catterall, Lattice supersymmetry and topological field theory 2003 J. High Energy Phys. JHEP05(2003)038 [hep-lat/0301028]
9. S. Catterall, A geometrical approach to N ≤ 2 super Yang-Mills theory on the two dimensional lattice 2004 J. High Energy Phys. JHEP11(2004)006 [hep-lat/0410052]
10. S. Catterall, Lattice formulation of N ≤ 4 super Yang-Mills theory 2005 J. High Energy Phys. JHEP06(2005)027 [hep-lat/0503036]
11. F. Sugino, A lattice formulation of super Yang-Mills theories with exact supersymmetry 2004 J. High Energy Phys. JHEP01(2004)015 [hep-lat/0311021]
12. F. Sugino, Super Yang-Mills theories on the two-dimensional lattice with exact supersymmetry 2004 J. High Energy Phys. JHEP03(2004)067 [hep-lat/0401017]
13. F. Sugino, Various super Yang-Mills theories with exact supersymmetry on the lattice 2005 J. High Energy Phys. JHEP01(2005)016 [hep-lat/0410035]
14. G. Bhanot, U.M. Heller and H. Neuberger, The quenched Eguchi-Kawai model 1982 Phys. Lett. B 113 47
15. M. Okawa, Monte Carlo study of the Eguchi-Kawai model 1982 Phys. Rev. Lett. 49 353
16. G. Parisi, A simple expression for planar field theories 1982 Phys. Lett. B 112 463
17. S.R. Das and S.R. Wadia, Translation invariance and a reduced model for summing planar diagrams in QCD 1982 Phys. Lett. B 117 228
18. M. Okawa, Monte Carlo study of the quenched Eguchi-Kawai model 1982 Phys. Rev. Lett. 49 705
19. D.J. Gross and Y. Kitazawa, A quenched momentum prescription for large-N theories 1982 Nucl. Phys. B 206 440
20. A. Gonzalez-Arroyo and M. Okawa, The twisted Eguchi-Kawai model: a reduced model for large-N lattice gauge theory 1983 Phys. Rev. D 27 2397
21. H. Aoki et al., Noncommutative Yang-Mills in IIB matrix model 2000 Nucl. Phys. B 565 176 [hep-th/9908141]
22. J. Ambjørn, Y.M. Makeenko, J. Nishimura and R.J. Szabo, Finite N matrix models of noncommutative gauge theory 1999 J. High Energy Phys. JHEP11(1999)029 [hep-th/9911041]
23. J. Ambjørn, Y.M. Makeenko, J. Nishimura and R.J. Szabo, Nonperturbative dynamics of noncommutative gauge theory 2000 Phys. Lett. B 480 399 [hep-th/0002158]
24. J. Ambjørn, Y.M. Makeenko, J. Nishimura and R.J. Szabo, Lattice gauge fields and discrete noncommutative Yang-Mills theory 2000 J. High Energy Phys. JHEP05(2000)023 [hep-th/0004147]
25. A. Gonzalez-Arroyo and C.P. Korthals Altes, Reduced model for large-N continuum field theories 1983 Phys. Lett. B 131 396
26. R. Narayanan and H. Neuberger, Large-N reduction in continuum 2003 Phys. Rev. Lett. 91 081601 [hep-lat/0303023]
27. c 2004 Nucl. Phys. B 696 107 [hep-lat/0405025]
28. R. Narayanan and H. Neuberger, The quark mass dependence of the pion mass at infinite N 2005 Phys. Lett. B 616 76 [hep-lat/0503033]
29. J. Kiskis, R. Narayanan and H. Neuberger, Proposal for the numerical solution of planar QCD 2002 Phys. Rev. D 66 025019 [hep-lat/0203005]
30. J. Kiskis, R. Narayanan and H. Neuberger, Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N? 2003 Phys. Lett. B 574 65 [hep-lat/0308033]
31. T.D. Cohen, Large-N(c) continuum reduction and the thermodynamics of QCD 2004 Phys. Rev. Lett. 93 201601 [hep-ph/0407306]
32. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M-theory as a matrix model: a conjecture 1997 Phys. Rev. D 55 5112 [hep-th/9610043]
33. E. Witten, String theory dynamics in various dimensions 1995 Nucl. Phys. B 443 85 [hep-th/9503124]
34. M. Claudson and M.B. Halpern, Supersymmetric ground state wave functions 1985 Nucl. Phys. B 250 689
35. E. Witten, Bound states of strings and p-branes 1996 Nucl. Phys. B 460 335 [hep-th/9510135]
36. R.A. Janik and J. Wosiek, Towards the matrix model of M-theory on a lattice 2001 Acta Phys. Polon. B 32 2143 [hep-th/0003121]
37. P. Bialas and J. Wosiek, Towards the lattice study of M-theory. II 2002 Nucl. Phys. (Proc. Suppl.) 106 968 [hep-lat/0111034]
38. O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, Black hole - black string phase transitions in thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle 2004 Class. Quantum Grav. 21 5169 [hep-th/0406210]
39. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring 1997 Nucl. Phys. B 498 467 [hep-th/9612115]
40. J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model 2002 J. High Energy Phys. JHEP05(2002)001 [hep-th/0111102]
41. 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 2002 Nucl. Phys. B 647 153 [hep-th/0204240]
42. H. Kawai, S. Kawamoto, T. Kuroki and S. Shinohara, Improved perturbation theory and four-dimensional space-time in IIB matrix model 2003 Prog. Theor. Phys. 109 115 [hep-th/0211272]
43. T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large-N reduced models 1999 Nucl. Phys. B 545 543 [hep-th/9811220]
44. Y.M. Makeenko, Methods of contemporary gauge theory Cambridge, U.K., 2002
45. W. Krauth and M. Staudacher, Finite Yang-Mills integrals 1998 Phys. Lett. B 435 350 [hep-th/9804199]
46. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Large-N dynamics of dimensionally reduced 4D SU(N) super Yang-Mills theory, 2000 J. High Energy Phys. JHEP07(2000)013 [hep-th/0003208]
47. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, F. Hofheinz and J. Nishimura, On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings 2002 Phys. Rev. D 65 086001 [hep-th/0104260]
48. Z. Burda, B. Petersson and M. Wattenberg, Semiclassical geometry of 4D reduced supersymmetric Yang-Mills integrals 2005 J. High Energy Phys. JHEP03(2005)058 [hep-th/0503032]
49. H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Space-time structures from IIB matrix model 1998 Prog. Theor. Phys. 99 713 [hep-th/9802085]
50. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Monte Carlo studies of the IIB matrix model at large N 2000 J. High Energy Phys. JHEP07(2000)011 [hep-th/0005147]
51. J. Nishimura and G. Vernizzi, Spontaneous breakdown of Lorentz invariance in IIB matrix model 2000 J. High Energy Phys. JHEP04(2000)015 [hep-th/0003223]
52. J. Nishimura and G. Vernizzi, Brane world from IIB matrices 2000 Phys. Rev. Lett. 85 4664 [hep-th/0007022]
53. Z. Burda, B. Petersson and J. Tabaczek, Geometry of reduced supersymmetric 4D Yang-Mills integrals 2001 Nucl. Phys. B 602 399 [hep-lat/0012001]
54. J. Nishimura, Exactly solvable matrix models for the dynamical generation of space-time in superstring theory 2002 Phys. Rev. D 65 105012 [hep-th/0108070]
55. K.N. Anagnostopoulos and J. Nishimura, New approach to the complex-action problem and its application to a nonperturbative study of superstring theory 2002 Phys. Rev. D 66 106008 [hep-th/0108041]
56. G. Vernizzi and J.F. Wheater, Rotational symmetry breaking in multi-matrix models 2002 Phys. Rev. D 66 085024 [hep-th/0206226]
57. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Effective actions of matrix models on homogeneous spaces 2004 Nucl. Phys. B 679 143 [hep-th/0307007]
58. J. Nishimura, Lattice superstring and noncommutative geometry 2004 Nucl. Phys. (Proc. Suppl.) 129 121 [hep-lat/0310019]
59. 2 geometry in IIB matrix model 2004 Nucl. Phys. B 686 248 [hep-th/0312241]
60. J. Nishimura, T. Okubo and F. Sugino, Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry [hep-th/0412194]
61. S. Bal, M. Hanada, H. Kawai and F. Kubo, Fuzzy torus in matrix model [hep-th/0412303]
62. 2 in IIB type matrix models 2005 Nucl. Phys. B 725 93 [hep-th/0506033]
63. W. Taylor, D-brane field theory on compact spaces 1997 Phys. Lett. B 394 283 [hep-th/9611042]
64. L. Motl, Proposals on nonperturbative superstring interactions [hep-th/9701025]
65. R. Dijkgraaf, E. Verlinde and H. Verlinde, Matrix string theory 1997 Nucl. Phys. B 500 43 [hep-th/9703030]
66. D.J. Gross and E. Witten, Possible third order phase transition in the large-N lattice gauge theory 1980 Phys. Rev. D 21 446