Convergence of the gaussian expansion method in dimensionally reduced Yang-Mills integrals

Journal of High Energy Physics

Volumn 6, Issue 10, 2002, Pages 979-994

  Nishimura, Jun ^a   Okubo, Toshiyuki ^a   Sugino, Fumihiko ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b CEA SACLAY   (France)

Author keywords

Matrix Models; Superstring Vacua; Superstrings and Heterotic Strings

Indexed keywords

EID: 23044455267     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2002/10/043     Document Type: Article

References (39)

1. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115].
2. W. Krauth, H. Nicolai and M. Staudacher, Monte Carlo approach to M-theory, Phys. Lett. B 431 (1998) 31 [hep-th/9803117];
3. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Monte Carlo studies of the IIB matrix model at large-N, J. High Energy Phys. 07 (2000) 011 [hep-th/0005147];
4. P. Bialas, Z. Burda, B. Petersson and J. Tabaczek, Large-N limit of the IKKT matrix model, Nucl. Phys. B 592 (2001) 391 [hep-lat/0007013];
5. Z. Burda, B. Petersson and J. Tabaczek, Geometry of reduced supersymmetric 4d Yang-Mills integrals, Nucl. Phys. B 602 (2001) 399 [hep-lat/0012001];
6. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, F. Hofheinz and J. Nishimura, On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings, Phys. Rev. D 65 (2002) 086001 [hep-th/0104260].
7. 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, J. High Energy Phys. 07 (2000) 013 [hep-th/0003208].
8. J. Nishimura and G. Vernizzi, Spontaneous breakdown of Lorentz invariance in IIB matrix model, J. High Energy Phys. 04 (2000) 015 [hep-th/0003223];
9. Brane world from IIB matrices, Phys. Rev. Lett. 85 (2000) 4664 [hep-th/0007022];
10. J. Nishimura, Exactly solvable matrix models for the dynamical generation of space-time in superstring theory, Phys. Rev. D 65 (2002) 105012 [hep-th/0108070].
11. K.N. Anagnostopoulos and J. Nishimura, A new solution of the complex action problem and the dynamical space-time in the IIB matrix model, hep-th/0108041.
12. A. Iucci and C. Naán, Conformal gaussian approximation, hep-th/0109118.
13. J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, J. Hig Energy Phys. 05 (2002) 001 [hep-th/0111102].
14. 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, hep-th/0204240.
15. M. Engelhardt and S. Levit, Variational master field for large-N interacting matrix models: free random variables on trial, Nucl. Phys. B 488 (1997) 735 [hep-th/9609216].
16. D. Kabat and G. Lifschytz, Approximations for strongly-coupled supersymmetric quantum mechanics, Nucl. Phys. B 571 (2000) 419 [hep-th/9910001].
17. D. Kabat, G. Lifschytz and D.A. Lowe, Black hole thermodynamics from calculations in strongly coupled gauge theory, Phys. Rev. Lett. 86 (2001) 1426 [hep-th/0007051];
18. Black hole entropy from non-perturbative gauge theory, Phys. Rev. D 64 (2001) 124015 [hep-th/0105171];
19. N. Iizuka, D. Kabat, G. Lifschytz and D.A. Lowe, Probing black holes in non-perturbative gauge theory, Phys. Rev. D 65 (2002) 024012 [hep-th/0108006].
20. W. Krauth and M. Staudacher, Finite Yang-Mills integrals, Phys. Lett. B 435 (1998) 350 [hep-th/9804199].
21. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory, Phys. Rev. Lett. 48 (1982) 1063.
22. K.N. Anagnostopoulos, W. Bietenholz and J. Nishimura, The area law in matrix models for large-N QCD strings, Int. J. Mod. Phys. C 13 (2002) 555 [hep-lat/0112035].
23. T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large-N reduced models, Nucl. Phys. B 545 (1999) 543 [hep-th/9811220].
24. W.E. Caswell, Accurate energy levels for the anharmonic oscillator and a summable series for the double well potential in perturbation theory, Ann. Phys. (NY) 123 (1979) 153;
25. I.G. Halliday and P. Suranyi, The anharmonic oscillator: a new approach, Phys. Rev. D 21 (1980) 1529;
26. J. Killingbeck, Renormalised perturbation series, J. Phys. A 14 (1981) 1005.
27. P.M. Stevenson, Optimized perturbation theory, Phys. Rev. D 23 (1981) 2916.
28. P.M. Stevenson, Optimization and the ultimate convergence of QCD perturbation theory, Nucl. Phys. B 231 (1984) 65;
29. I.R.C. Buckley, A. Duncan and H.F. Jones, Proof of the convergence of the linear delta expansion, Phys. Rev. D 47 (1993) 2554;
30. A. Duncan and H.F. Jones, Convergence proof for optimized delta expansion: the anharmonic oscillator, Phys. Rev. D 47 (1993) 2560;
31. C.M. Bender, A. Duncan and H.F. Jones, Convergence of the optimized delta expansion for the connected vacuum amplitude: zero dimensions, Phys. Rev. D 49 (1994) 4219 [hep-th/9310031];
32. R. Guida, K. Konishi and H. Suzuki, Convergence of scaled delta expansion: anharmonic oscillator, Ann. Phys. (NY) 241 (1995) 152 [hep-th/9407027];
33. Improved convergence proof of the delta expansion and order dependent mappings, Ann. Phys. (NY) 249 (1996) 109 [hep-th/9505084].
34. E. Braaten and E. Radescu, Convergence of the linear delta expansion in the critical O(N) field theory, hep-ph/0206108.
35. P. Austing and J.F. Wheater, The convergence of Yang-Mills integrals, J. High Energy Phys. 02 (2001) 028 [hep-th/0101071].
36. S. Oda and F. Sugino, Gaussian and mean field approximations for reduced Yang-Mills integrals, J. High Energy Phys. 03 (2001) 026 [hep-th/0011175].
37. F. Sugino, Gaussian and mean field approximations for reduced 4d supersymmetric Yang-Mills integral, J. High Energy Phys. 07 (2001) 014 [hep-th/0105284].
38. J. Nishimura, K. Nishiyama, T. Okubo and F. Sugino, work in progress.
39. 4 theory, Phys. Rev. D 42 (1990) 2710.