Exact fuzzy sphere thermodynamics in matrix quantum mechanics

Journal of High Energy Physics

Volumn 2007, Issue 5, 2007, Pages

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

^a HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

^c GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

Author keywords

Matrix models; Non commutative geometry; Thermal field theory

Indexed keywords

EID: 34547604298     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/05/091     Document Type: Article

References (88)

1. J. Madore, The fuzzy sphere, 1992 Class. Quantum Grav. 9 69
2. N. Seiberg and E. Witten, String theory and noncommutative geometry 1999 J. High Energy Phys. JHEP09(1999)032 [hep-th/9908142]
3. S. Doplicher, K. Fredenhagen and J.E. Roberts, The quantum structure of spacetime at the Planck scale and quantum fields 1995 Comm. Math. Phys. 172 187 [hep-th/0303037]
4. H. Grosse, C. Klimcik and P. Presnajder, Towards finite quantum field theory in noncommutative geometry 1996 Int. J. Theor. Phys. 35 231 [hep-th/9505175]
5. R.C. Myers, Dielectric-branes 1999 J. High Energy Phys. JHEP12(1999)022 [hep-th/9910053]
6. D. Bak, Supersymmetric branes in pp wave background 2003 Phys. Rev. D 67 045017 [hep-th/0204033]
7. S. Hyun and H. Shin, Branes from matrix theory in pp-wave background 2002 Phys. Lett. B 543 115 [hep-th/0206090]
8. J.H. Park, Supersymmetric objects in the M-theory on a pp-wave 2002 J. High Energy Phys. JHEP10(2002)032 [hep-th/0208161]
9. D. Bak, S. Kim and K. Lee, All higher genus BPS membranes in the plane wave background 2005 J. High Energy Phys. JHEP06(2005)035 [hep-th/0501202]
10. H. Shin and K. Yoshida, One-loop flatness of membrane fuzzy sphere interaction in plane-wave matrix model 2004 Nucl. Phys. B 679 99 [hep-th/0309258]
11. H. Shin and K. Yoshida, Membrane fuzzy sphere dynamics in plane-wave matrix model 2005 Nucl. Phys. B 709 69 [hep-th/0409045]
12. D. Berenstein, J.M. Maldacena and H. Nastase, Strings in flat space and pp waves from N ≤ 4 super Yang Mills 2002 J. High Energy Phys. JHEP04(2002)013 [hep-th/0202021]
13. 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]
14. J. Kowalski-Glikman, Vacuum states in supersymmetric Kaluza-Klein theory 1984 Phys. Lett. B 134 194
15. K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Matrix perturbation theory for M-theory on a PP-wave 2002 J. High Energy Phys. JHEP05(2002)056 [hep-th/0205185]
16. K. Sugiyama and K. Yoshida, Giant graviton and quantum stability in matrix model on PP-wave background 2002 Phys. Rev. D 66 085022 [hep-th/0207190]
17. K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Protected multiplets of M-theory on a plane wave 2002 J. High Energy Phys. JHEP09(2002)021 [hep-th/0207050]
18. N. Kim and J. Plefka, On the spectrum of pp-wave matrix theory 2002 Nucl. Phys. B 643 31 [hep-th/0207034]
19. N. Kim and J.H. Park, Superalgebra for M-theory on a pp-wave 2002 Phys. Rev. D 66 106007 [hep-th/0207061]
20. R. Dijkgraaf, E. Verlinde and H. Verlinde, Matrix string theory 1997 Nucl. Phys. B 500 43 [hep-th/9703030]
21. K. Sugiyama and K. Yoshida, Type IIA string and matrix string on pp-wave 2002 Nucl. Phys. B 644 128 [hep-th/0208029]
22. S.R. Das, J. Michelson and A.D. Shapere, Fuzzy spheres in pp-wave matrix string theory 2004 Phys. Rev. D 70 026004 [hep-th/0306270]
23. S. R. Das and J. Michelson, pp wave big bangs: Matrix strings and shrinking fuzzy spheres 2005 Phys. Rev. D 72 086005 [hep-th/0508068]
24. K. Furuuchi, E. Schreiber and G.W. Semenoff, Five-brane thermodynamics from the matrix model [hep-th/0310286]
25. J. Maldacena, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Transverse fivebranes in matrix theory 2003 J. High Energy Phys. JHEP01(2003)038 [hep-th/0211139]
26. Y. Lozano and D. Rodriguez-Gomez, Fuzzy 5-spheres and pp-wave matrix actions 2005 J. High Energy Phys. JHEP08(2005)044 [hep-th/0505073]
27. M. Spradlin, M. Van Raamsdonk and A. Volovich, Two-loop partition function in the planar plane-wave matrix model 2004 Phys. Lett. B 603 239 [hep-th/0409178]
28. S. Hadizadeh, B. Ramadanovic, G.W. Semenoff and D. Young, Free energy and phase transition of the matrix model on a plane-wave 2005 Phys. Rev. D 71 065016 [hep-th/0409318]
29. G.W. Semenoff, Matrix model thermodynamics [hep-th/0405107]
30. W.H. Huang, Thermal instability of giant graviton in matrix model on pp-wave background 2004 Phys. Rev. D 69 067701 [hep-th/0310212]
31. H. Shin and K. Yoshida, Thermodynamics of fuzzy spheres in pp-wave matrix model 2004 Nucl. Phys. B 701 380 [hep-th/0401014]
32. H. Shin and K. Yoshida, Thermodynamic behavior of fuzzy membranes in pp-wave matrix model 2005 Phys. Lett. B 627 188 [hep-th/0507029]
33. N. Kawahara, J. Nishimura and K. Yoshida, Dynamical aspects of the plane-wave matrix model at finite temperature 2006 J. High Energy Phys. JHEP0123(2006)001 [hep-th/0601170]
34. A. Agarwal, Mass-gaps and spin chains for (super) membranes [hep-th/0610014]
35. R. A. Janik and J. Wosiek, Towards the matrix model of M-theory on a lattice 2001 Acta Phys. Polon. 32 2143 [hep-th/0003121]
36. P. Bialas and J. Wosiek, Lattice study of the simplified model of M-theory [hep-lat/0105031]
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. P. Bialas and J. Wosiek, Lattice study of the simplified model of M-theory for larger gauge groups [hep-lat/0109031]
39. O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large N gauge theories 2004 Adv. Theor. Math. Phys. 8 603 [hep-th/0310285]
40. 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]
41. 3 2005 Phys. Rev. D 71 125018 [hep-th/0502149]
42. O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, M. Van Raamsdonk and T. Wiseman, The phase structure of low dimensional large N gauge theories on tori 2006 J. High Energy Phys. JHEP01(2006)140 [hep-th/0508077]
43. 5 and critical unitary matrix models 2006 Eur. Phys. J. C 48 647 [hep-th/0605041]
44. B. Lucini, M. Teper and U. Wenger, Properties of the deconfining phase transition in SU(N) gauge theories 2005 J. High Energy Phys. JHEP02(2005)033 [hep-lat/0502003]
45. J. Ambjorn, Y.M. Makeenko and G. W. Semenoff, Thermodynamics of D0-branes in matrix theory 1999 Phys. Lett. B 445 307 [hep-th/9810170]
46. Y. Makeenko, Formulation of matrix theory at finite temperature 2000 Fortsch. Phys. 48 171 [hep-th/9903030]
47. M. Li, Ten dimensional black hole and the D0-brane threshold bound state 1999 Phys. Rev. D 60 066002 [hep-th/9901158]
48. D. Kabat, G. Lifschytz and D.A. Lowe, Black hole thermodynamics from calculations in strongly coupled gauge theory 2001 Phys. Rev. Lett. 86 1426 [hep-th/0007051]
49. I.R. Klebanov and L. Susskind, Schwarzschild black holes in various dimensions from matrix theory 1998 Phys. Lett. B 416 62 [hep-th/9709108]
50. T. Banks, W. Fischler, I.R. Klebanov and L. Susskind, Schwarzschild black holes in matrix theory. II 1998 J. High Energy Phys. JHEP01(1998)008 [hep-th/9711005]
51. N. Itzhaki, J. M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges 1998 Phys. Rev. D 58 046004 [hep-th/9802042]
52. Y. Kitazawa, Y. Takayama and D. Tomino, Correlators of matrix models on homogeneous spaces 2004 Nucl. Phys. B 700 183 [hep-th/0403242]
53. T. Azuma, K. Nagao and J. Nishimura, Perturbative dynamics of fuzzy spheres at large N 2005 J. High Energy Phys. JHEP06(2005)081 [hep-th/0410263]
54. 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]
55. T. Azuma, S. Bal, K. Nagao and J. Nishimura, Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term 2004 J. High Energy Phys. JHEP05(2004)005 [hep-th/0401038]
56. 2 in the large N reduced model with a cubic term 2006 J. High Energy Phys. JHEP05(2006)061 [hep-th/0405277]
57. T. Azuma, S. Bal, K. Nagao and J. Nishimura
58. 2, 2005 J. High Energy Phys. JHEP09(2005)047 [hep-th/0506205]
59. N. Kawahara, J. Nishimura and S. Takeuchi, Monte Carlo studies of matrix quantum mechanics at finite temperature in preparation
60. N. Kawahara and J. Nishimura, The large N reduction in matrix quantum mechanics: a bridge between BFSS and IKKT 2005 J. High Energy Phys. JHEP09(2005)040 [hep-th/0505178]
61. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large N gauge theory 1982 Phys. Rev. Lett. 48 1063
62. T. Reisz, Realization of dimensional reduction at high temperature 1992 Z. Physik C 53 169
63. 3 2005 Nucl. Phys. B 704 208 [hep-lat/0403027]
64. S. Bal and B. Sathiapalan, High temperature limit of the N ≤ 2 matrix model 1999 Mod. Phys. Lett. A 14 2753 [hep-th/9902087]
65. N. Kawahara, J. Nishimura and S. Takeuchi, High temperature expansion in supersymmetric quantum mechanics in preparation
66. T. Hotta, J, Nishimura and A. Tsuchiya, Dynamical aspects of large N reduced models 1999 Nucl. Phys. B 545 543 [hep-th/9811220]
67. Y. Kitazawa, Matrix models in homogeneous spaces 2002 Nucl. Phys. B 642 210 [hep-th/0207115]
68. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Quantum corrections on fuzzy sphere 2003 Nucl. Phys. B 665 520 [hep-th/0303120]
69. 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]
70. 2 geometry in IIB matrix model 2004 Nucl. Phys. B 686 248 [hep-th/0312241]
71. 2 in IIB type matrix models 2005 Nucl. Phys. B 725 93 [hep-th/0506033]
72. H. Kaneko, Y. Kitazawa and D. Tomino, Fuzzy spacetime with SU(3) isometry in IIB matrix model, 2006 Phys. Rev. D 73 066001 [hep-th/0510263]
73. 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]
74. J. Ambjorn, 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]
75. Z. Burda, B. Petersson and J. Tabaczek, Geometry of reduced supersymmetric 4D Yang-Mills integrals 2001 Nucl. Phys. B 602 399 [hep-lat/0012001]
76. J. Ambjorn, 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]
77. 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]
78. 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]
79. 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]
80. J. Nishimura and G. Vernizzi, Brane world generated dynamically from string type IIB matrices 2000 Phys. Rev. Lett. 85 4664 [hep-th/0007022]
81. 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]
82. 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]
83. 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]
84. 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]
85. 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]
86. T. Aoyama, H. Kawai and Y. Shibusa, Stability of 4-dimensional space-time from IIB matrix model via improved mean field approximation 2006 Prog. Theor. Phys. 115 1179 [hep-th/0602244]
87. T. Aoyama and H. Kawai, Higher order terms of improved mean field approximation for IIB matrix model and emergence of four-dimensional space-time 2006 Prog. Theor. Phys. 116 405 [hep-th/0603146]
88. T. Aoyama and Y. Shibusa, Improved perturbation method and its application to the IIB matrix model 2006 Nucl. Phys. B 754 48 [hep-th/0604211]