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Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models

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Abstract

It has long been speculated that the spontaneous symmetry breaking (SSB) of SO(D) occurs in matrix models obtained by dimensionally reducing super Yang-Mills theory in D = 6, 10 dimensions. In particular, the D = 10 case corresponds to the IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory, and the SSB may correspond to the dynamical generation of four-dimensional space-time. Recently, it has been shown by using the Gaussian expansion method that the SSB indeed occurs for D = 6 and D = 10, and interesting nature of the SSB common to both cases has been suggested. Here we study the same issue from first principles by a Monte Carlo method in the D = 6 case. In spite of a severe complex-action problem, the factorization method enables us to obtain various quantities associated with the SSB, which turn out to be consistent with the previous results obtained by the Gaussian expansion method. This also demonstrates the usefulness of the factorization method as a general approach to systems with the complex-action problem or the sign problem.

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References

  1. J. Nishimura, The origin of space-time as seen from matrix model simulations, Prog. Theor. Exp. Phys. 2012 (2012) 01A101 [arXiv:1205.6870] [INSPIRE].

    Article  Google Scholar 

  2. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. H. Aoki et al., IIB matrix model, Prog. Theor. Phys. Suppl. 134 (1999) 47 [hep-th/9908038] [INSPIRE].

    Article  ADS  Google Scholar 

  4. T. Azuma, Matrix models and the gravitational interaction, hep-th/0401120 [INSPIRE].

  5. H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Space-time structures from IIB matrix model, Prog. Theor. Phys. 99 (1998) 713 [hep-th/9802085] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] hep-th/9711200] [INSPIRE].

  7. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. M. Hanada, J. Nishimura and S. Takeuchi, Non-lattice simulation for supersymmetric gauge theories in one dimension, Phys. Rev. Lett. 99 (2007) 161602 [arXiv:0706.1647] [INSPIRE].

    Article  ADS  Google Scholar 

  9. S. Catterall and T. Wiseman, Towards lattice simulation of the gauge theory duals to black holes and hot strings, JHEP 12 (2007) 104 [arXiv:0706.3518] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. K.N. Anagnostopoulos, M. Hanada, J. Nishimura and S. Takeuchi, Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature, Phys. Rev. Lett. 100 (2008) 021601 [arXiv:0707.4454] [INSPIRE].

    Article  ADS  Google Scholar 

  11. S. Catterall and T. Wiseman, Black hole thermodynamics from simulations of lattice Yang-Mills theory, Phys. Rev. D 78 (2008) 041502 [arXiv:0803.4273] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. M. Hanada, Y. Hyakutake, J. Nishimura and S. Takeuchi, Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 191602 [arXiv:0811.3102] [INSPIRE].

    Article  ADS  Google Scholar 

  13. S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP 04 (2010) 077 [arXiv:0909.4947] [INSPIRE].

    Article  ADS  Google Scholar 

  14. M. Hanada, A. Miwa, J. Nishimura and S. Takeuchi, Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 181602 [arXiv:0811.2081] [INSPIRE].

    Article  ADS  Google Scholar 

  15. M. Hanada, J. Nishimura, Y. Sekino and T. Yoneya, Monte Carlo studies of Matrix theory correlation functions, Phys. Rev. Lett. 104 (2010) 151601 [arXiv:0911.1623] [INSPIRE].

    Article  ADS  Google Scholar 

  16. M. Hanada, J. Nishimura, Y. Sekino and T. Yoneya, Direct test of the gauge-gravity correspondence for Matrix theory correlation functions, JHEP 12 (2011) 020 [arXiv:1108.5153] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. Y. Sekino and T. Yoneya, Generalized AdS/CFT correspondence for matrix theory in the large-N limit, Nucl. Phys. B 570 (2000) 174 [hep-th/9907029] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. W. Krauth, H. Nicolai and M. Staudacher, Monte Carlo approach to M-theory, Phys. Lett. B 431 (1998) 31 [hep-th/9803117] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. W. Krauth and M. Staudacher, Finite Yang-Mills integrals, Phys. Lett. B 435 (1998) 350 [hep-th/9804199] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. P. Austing and J.F. Wheater, The convergence of Yang-Mills integrals, JHEP 02 (2001) 028 [hep-th/0101071] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. P. Austing and J.F. Wheater, Convergent Yang-Mills matrix theories, JHEP 04 (2001) 019 [hep-th/0103159] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, JHEP 05 (2002) 001 [hep-th/0111102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. 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, Nucl. Phys. B 647 (2002) 153 [hep-th/0204240] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. H. Kawai, S. Kawamoto, T. Kuroki and S. Shinohara, Improved perturbation theory and four-dimensional space-time in IIB matrix model, Prog. Theor. Phys. 109 (2003) 115 [hep-th/0211272] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. T. Aoyama and H. Kawai, Higher order terms of improved mean field approximation for IIB matrix model and emergence of four-dimensional space-time, Prog. Theor. Phys. 116 (2006) 405 [hep-th/0603146] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  29. J. Nishimura, T. Okubo and F. Sugino, Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings, JHEP 10 (2011) 135 [arXiv:1108.1293] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. J. Nishimura and G. Vernizzi, Spontaneous breakdown of Lorentz invariance in IIB matrix model, JHEP 04 (2000) 015 [hep-th/0003223] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. J. Nishimura and G. Vernizzi, Brane world generated dynamically from string type IIB matrices, Phys. Rev. Lett. 85 (2000) 4664 [hep-th/0007022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. K.N. Anagnostopoulos and J. Nishimura, New approach to the complex action problem and its application to a nonperturbative study of superstring theory, Phys. Rev. D 66 (2002) 106008 [hep-th/0108041] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions, Phys. Rev. Lett. 108 (2012) 011601 [arXiv:1108.1540] [INSPIRE].

    Article  ADS  Google Scholar 

  34. H. Steinacker, Split noncommutativity and compactified brane solutions in matrix models, Prog. Theor. Phys. 126 (2011) 613 [arXiv:1106.6153] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  35. A. Chatzistavrakidis, On Lie-algebraic solutions of the type IIB matrix model, Phys. Rev. D 84 (2011) 106010 [arXiv:1108.1107] [INSPIRE].

    ADS  Google Scholar 

  36. A.P. Polychronakos, H. Steinacker and J. Zahn, Brane compactifications and 4-dimensional geometry in the IKKT model, Nucl. Phys. B 875 (2013) 566 [arXiv:1302.3707] [INSPIRE].

    Article  ADS  Google Scholar 

  37. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory, Phys. Rev. D 86 (2012) 027901 [arXiv:1110.4803] [INSPIRE].

    ADS  Google Scholar 

  38. S.-W. Kim, J. Nishimura and A. Tsuchiya, Late time behaviors of the expanding universe in the IIB matrix model, JHEP 10 (2012) 147 [arXiv:1208.0711] [INSPIRE].

    Article  ADS  Google Scholar 

  39. J. Nishimura and A. Tsuchiya, Local field theory from the expanding universe at late times in the IIB matrix model, Prog. Theor. Exp. Phys. 2013 (2013) 043B03 [arXiv:1208.4910] [INSPIRE].

    Article  Google Scholar 

  40. H. Aoki, Chiral fermions and the standard model from the matrix model compactified on a torus, Prog. Theor. Phys. 125 (2011) 521 [arXiv:1011.1015] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  41. H. Aoki, Probability of the standard model appearance from a matrix model, Phys. Rev. D 87 (2013) 046002 [arXiv:1209.4514] [INSPIRE].

    ADS  Google Scholar 

  42. H. Aoki, Probability distribution over some phenomenological models in the matrix model compactified on a torus, Prog. Theor. Exp. Phys. 2013 (2013) 0903B04 [arXiv:1303.3982] [INSPIRE].

    Article  Google Scholar 

  43. A. Chatzistavrakidis, H. Steinacker and G. Zoupanos, Intersecting branes and a standard model realization in matrix models, JHEP 09 (2011) 115 [arXiv:1107.0265] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. J. Nishimura and A. Tsuchiya, Realizing chiral fermions in the type IIB matrix model at finite N, arXiv:1305.5547 [INSPIRE].

  45. T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large-N reduced models, Nucl. Phys. B 545 (1999) 543 [hep-th/9811220] [INSPIRE].

    Article  ADS  Google Scholar 

  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, JHEP 07 (2000) 013 [hep-th/0003208] [INSPIRE].

    Article  ADS  Google Scholar 

  47. J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Monte Carlo studies of the IIB matrix model at large N, JHEP 07 (2000) 011 [hep-th/0005147] [INSPIRE].

    Article  ADS  Google Scholar 

  48. 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] [INSPIRE].

    ADS  Google Scholar 

  49. 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] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  50. Z. Burda, B. Petersson and J. Tabaczek, Geometry of reduced supersymmetric 4-D Yang-Mills integrals, Nucl. Phys. B 602 (2001) 399 [hep-lat/0012001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. J. Ambjørn, K.N. Anagnostopoulos, J. Nishimura and J.J.M. Verbaarschot, The factorization method for systems with a complex action: a test in random matrix theory for inite density QCD, JHEP 10 (2002) 062 [hep-lat/0208025] [INSPIRE].

    Article  ADS  Google Scholar 

  52. J. Ambjørn, K.N. Anagnostopoulos, J. Nishimura and J.J.M. Verbaarschot, Noncommutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems, Phys. Rev. D 70 (2004) 035010 [hep-lat/0402031] [INSPIRE].

    ADS  Google Scholar 

  53. V. Azcoiti, G. Di Carlo, A. Galante and V. Laliena, New proposal for numerical simulations of θ-vacuum-like systems, Phys. Rev. Lett. 89 (2002) 141601 [hep-lat/0203017] [INSPIRE].

    Article  ADS  Google Scholar 

  54. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, A general approach to the sign problem: the factorization method with multiple observables, Phys. Rev. D 83 (2011) 054504 [arXiv:1009.4504] [INSPIRE].

    ADS  Google Scholar 

  55. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, A study of the complex action problem in a simple model for dynamical compactification in superstring theory using the factorization method, PoS(Lattice 2010)167 [arXiv:1010.0957] [INSPIRE].

  56. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, A practical solution to the sign problem in a matrix model for dynamical compactification, JHEP 10 (2011) 126 [arXiv:1108.1534] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, Towards an effective importance sampling in Monte Carlo simulations of a system with a complex action, PoS(Lattice 2011)181 [arXiv:1110.6531] [INSPIRE].

  58. Z. Fodor, S.D. Katz and C. Schmidt, The density of states method at non-zero chemical potential, JHEP 03 (2007) 121 [hep-lat/0701022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. Z. Fodor and S.D. Katz, A new method to study lattice QCD at finite temperature and chemical potential, Phys. Lett. B 534 (2002) 87 [hep-lat/0104001] [INSPIRE].

    Article  ADS  Google Scholar 

  60. Z. Fodor and S.D. Katz, Critical point of QCD at finite T and μ, lattice results for physical quark masses, JHEP 04 (2004) 050 [hep-lat/0402006] [INSPIRE].

    Article  ADS  Google Scholar 

  61. S. Ejiri, On the existence of the critical point in finite density lattice QCD, Phys. Rev. D 77 (2008) 014508 [arXiv:0706.3549] [INSPIRE].

    ADS  Google Scholar 

  62. S. Ejiri, Phase structure of hot dense QCD by a histogram method, Eur. Phys. J. A 49 (2013) 86 [arXiv:1306.0295] [INSPIRE].

    Article  ADS  Google Scholar 

  63. M.P. Lombardo, K. Splittorff and J.J.M. Verbaarschot, Distributions of the phase angle of the fermion determinant in QCD, Phys. Rev. D 80 (2009) 054509 [arXiv:0904.2122] [INSPIRE].

    ADS  Google Scholar 

  64. M.P. Lombardo, K. Splittorff and J.J.M. Verbaarschot, The fluctuations of the quark number and of the chiral condensate, Phys. Rev. D 81 (2010) 045012 [arXiv:0910.5482] [INSPIRE].

    ADS  Google Scholar 

  65. J. Greensite, J.C. Myers and K. Splittorff, The QCD sign problem as a total derivative, Phys. Rev. D 88 (2013) 031502 [arXiv:1306.3085] [INSPIRE].

    ADS  Google Scholar 

  66. W. Unger and P. de Forcrand, Continuous time Monte Carlo for lattice QCD in the strong coupling limit, J. Phys. G 38 (2011) 124190 [arXiv:1107.1553] [INSPIRE].

    Article  ADS  Google Scholar 

  67. P. de Forcrand and O. Philipsen, Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential, Phys. Rev. Lett. 105 (2010) 152001 [arXiv:1004.3144] [INSPIRE].

    Article  ADS  Google Scholar 

  68. J. Bloch, A subset solution to the sign problem in random matrix simulations, Phys. Rev. D 86 (2012) 074505 [arXiv:1205.5500] [INSPIRE].

    ADS  Google Scholar 

  69. J. Bloch, Evading the sign problem in random matrix simulations, Phys. Rev. Lett. 107 (2011) 132002 [arXiv:1103.3467] [INSPIRE].

    Article  ADS  Google Scholar 

  70. J. Bloch and T. Wettig, The QCD sign problem and dynamical simulations of random matrices, JHEP 05 (2011) 048 [arXiv:1102.3715] [INSPIRE].

    Article  ADS  Google Scholar 

  71. G. Aarts, F.A. James, E. Seiler and I.-O. Stamatescu, Complex Langevin: etiology and diagnostics of its main problem, Eur. Phys. J. C 71 (2011) 1756 [arXiv:1101.3270] [INSPIRE].

    Article  ADS  Google Scholar 

  72. G. Aarts and F.A. James, On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential, JHEP 08 (2010) 020 [arXiv:1005.3468] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  73. G. Aarts, Can stochastic quantization evade the sign problem? The relativistic Bose gas at finite chemical potential, Phys. Rev. Lett. 102 (2009) 131601 [arXiv:0810.2089] [INSPIRE].

    Article  ADS  Google Scholar 

  74. G. Aarts and I.-O. Stamatescu, Stochastic quantization at finite chemical potential, JHEP 09 (2008) 018 [arXiv:0807.1597] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  75. S. Chandrasekharan and A. Li, Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions, JHEP 01 (2011) 018 [arXiv:1008.5146] [INSPIRE].

    Article  ADS  Google Scholar 

  76. C.R. Allton et al., The QCD thermal phase transition in the presence of a small chemical potential, Phys. Rev. D 66 (2002) 074507 [hep-lat/0204010] [INSPIRE].

    ADS  Google Scholar 

  77. R.V. Gavai and S. Gupta, Pressure and nonlinear susceptibilities in QCD at finite chemical potentials, Phys. Rev. D 68 (2003) 034506 [hep-lat/0303013] [INSPIRE].

    ADS  Google Scholar 

  78. M. D’Elia and M.-P. Lombardo, Finite density QCD via imaginary chemical potential, Phys. Rev. D 67 (2003) 014505 [hep-lat/0209146] [INSPIRE].

    ADS  Google Scholar 

  79. P. de Forcrand and O. Philipsen, The QCD phase diagram for small densities from imaginary chemical potential, Nucl. Phys. B 642 (2002) 290 [hep-lat/0205016] [INSPIRE].

    Article  ADS  Google Scholar 

  80. W. Bietenholz, A. Pochinsky and U.J. Wiese, Meron cluster simulation of the theta vacuum in the 2-d O(3) model, Phys. Rev. Lett. 75 (1995) 4524 [hep-lat/9505019] [INSPIRE].

    Article  ADS  Google Scholar 

  81. M. Creutz, Microcanonical Monte Carlo simulation, Phys. Rev. Lett. 50 (1983) 1411 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  82. G. Bhanot, K. Bitar and R. Salvador, On solving four-dimensional SU(2) gauge theory by numerically finding its partition function, Phys. Lett. B 188 (1987) 246 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  83. G. Bhanot, A. Gocksch and P. Rossi, On simulating complex actions, Phys. Lett. B 199 (1987) 101 [INSPIRE].

    Article  ADS  Google Scholar 

  84. A. Gocksch, Simulating lattice QCD at finite density, Phys. Rev. Lett. 61 (1988) 2054 [INSPIRE].

    Article  ADS  Google Scholar 

  85. M. Karliner, S.R. Sharpe and Y.F. Chang, Zeroing in on SU(3), Nucl. Phys. B 302 (1988) 204 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  86. A. Gocksch, The Riemann walk: a method for simulating complex actions, Phys. Lett. B 206 (1988) 290 [INSPIRE].

    Article  ADS  Google Scholar 

  87. 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] [INSPIRE].

    ADS  Google Scholar 

  88. J. Nishimura, T. Okubo and F. Sugino, Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry, Prog. Theor. Phys. 114 (2005) 487 [hep-th/0412194] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  89. T. Aoyama, J. Nishimura and T. Okubo, Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models, Prog. Theor. Phys. 125 (2011) 537 [arXiv:1007.0883] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  90. K.N. Anagnostopoulos, T. Azuma and J. Nishimura, Monte Carlo simulations of a supersymmetric matrix model of dynamical compactification in non perturbative string theory, PoS(Lattice 2012)226 [arXiv:1211.0950] [INSPIRE].

  91. A.D. Kennedy, I. Horvath and S. Sint, A new exact method for dynamical fermion computations with nonlocal actions, Nucl. Phys. Proc. Suppl. 73 (1999) 834 [hep-lat/9809092] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  92. M.A. Clark and A.D. Kennedy, The RHMC algorithm for two flavors of dynamical staggered fermions, Nucl. Phys. Proc. Suppl. 129 (2004) 850 [hep-lat/0309084] [INSPIRE].

    Article  ADS  Google Scholar 

  93. M.A. Clark, A.D. Kennedy and Z. Sroczynski, Exact 2+1 flavour RHMC simulations, Nucl. Phys. Proc. Suppl. 140 (2005) 835 [hep-lat/0409133] [INSPIRE].

    Article  ADS  Google Scholar 

  94. M.A. Clark and A.D. Kennedy, https://github.com/mikeaclark/AlgRemez (2005).

  95. S. Catterall and S. Karamov, Testing a Fourier accelerated hybrid Monte Carlo algorithm, Phys. Lett. B 528 (2002) 301 [hep-lat/0112025] [INSPIRE].

    Article  ADS  Google Scholar 

  96. B. Jegerlehner, Krylov space solvers for shifted linear systems, hep-lat/9612014 [INSPIRE].

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Authors and Affiliations

  1. Physics Department, National Technical University, Zografou Campus, GR-15780, Athens, Greece

    Konstantinos N. Anagnostopoulos

  2. Institute for Fundamental Sciences, Setsunan University, 17-8 Ikeda Nakamachi, Neyagawa, Osaka, 572-8508, Japan

    Takehiro Azuma

  3. KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

  4. Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

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  1. Konstantinos N. Anagnostopoulos
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Correspondence to Takehiro Azuma.

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Anagnostopoulos, K.N., Azuma, T. & Nishimura, J. Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models. J. High Energ. Phys. 2013, 9 (2013). https://doi.org/10.1007/JHEP11(2013)009

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