Advertisement

Partial Deconfinement

  • Masanori HanadaEmail author
  • Goro Ishiki
  • Hiromasa Watanabe
Open Access
Regular Article - Theoretical Physics
  • 39 Downloads

Abstract

We argue that the confined and deconfined phases in gauge theories are connected by a partially deconfined phase (i.e. SU(M) in SU(N), where M < N, is deconfined), which can be stable or unstable depending on the details of the theory. When this phase is unstable, it is the gauge theory counterpart of the small black hole phase in the dual string theory. Partial deconfinement is closely related to the Gross-Witten-Wadia transition, and is likely to be relevant to the QCD phase transition.

The mechanism of partial deconfinement is related to a generic property of a class of systems. As an instructive example, we demonstrate the similarity between the Yang-Mills theory/string theory and a mathematical model of the collective behavior of ants [Beekman et al., Proceedings of the National Academy of Sciences, 2001]. By identifying the D-brane, open string and black hole with the ant, pheromone and ant trail, the dynamics of two systems closely resemble with each other, and qualitatively the same phase structures are obtained.

Keywords

Black Holes in String Theory Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
  2. [2]
    L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorndeconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Hanada and J. Maltz, A proposal of the gauge theory description of the small Schwarzschild black hole in AdS 5×S 5, JHEP 02 (2017) 012 [arXiv:1608.03276] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  7. [7]
    D. Berenstein, Submatrix deconfinement and small black holes in AdS, JHEP 09 (2018) 054 [arXiv:1806.05729] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    C.T. Asplund and D. Berenstein, Small AdS black holes from SYM, Phys. Lett. B 673 (2009) 264 [arXiv:0809.0712] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    E. Berkowitz, M. Hanada and J. Maltz, Chaos in Matrix Models and Black Hole Evaporation, Phys. Rev. D 94 (2016) 126009 [arXiv:1602.01473] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  10. [10]
    E. Berkowitz, M. Hanada and J. Maltz, A microscopic description of black hole evaporation via holography, Int. J. Mod. Phys. D 25 (2016) 1644002 [arXiv:1603.03055] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    J. Liddle and M. Teper, The deconfining phase transition in D = 2+1 SU(N) gauge theories, arXiv:0803.2128 [INSPIRE].
  12. [12]
    B. Lucini, M. Teper and U. Wenger, The high temperature phase transition in SU(N) gauge theories, JHEP 01 (2004) 061 [hep-lat/0307017] [INSPIRE].
  13. [13]
    L. Álvarez-Gaumé, P. Basu, M. Mariño and S.R. Wadia, Blackhole/String Transition for the Small Schwarzschild Blackhole of AdS 5 x S 5 and Critical Unitary Matrix Models, Eur. Phys. J. C 48 (2006) 647 [hep-th/0605041] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Beekman, D.J.T. Sumpter and F.L.W. Ratnieks, Phase transition between disordered and ordered foraging in Pharaohs ants, Proc. Nat. Acad. Sci. 98 (2001) 9703.ADSCrossRefGoogle Scholar
  15. [15]
    L. Kofman, A.D. Linde, X. Liu, A. Maloney, L. McAllister and E. Silverstein, Beauty is attractive: Moduli trapping at enhanced symmetry points, JHEP 05 (2004) 030 [hep-th/0403001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    D.J. Gross and E. Witten, Possible Third Order Phase Transition in the Large N Lattice Gauge Theory, Phys. Rev. D 21 (1980) 446 [INSPIRE].ADSGoogle Scholar
  18. [18]
    S.R. Wadia, A Study of U(N) Lattice Gauge Theory in 2-dimensions, arXiv:1212.2906 [INSPIRE].
  19. [19]
    S.R. Wadia, N = Infinity Phase Transition in a Class of Exactly Soluble Model Lattice Gauge Theories, Phys. Lett. 93B (1980) 403 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].Google Scholar
  21. [21]
    B. Sundborg, Strings hot fast and heavy, Institute of Theoretical Physics, (1988), https://gupea.ub.gu.se/handle/2077/14375.
  22. [22]
    L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
  23. [23]
    G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev. D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].ADSMathSciNetGoogle Scholar
  24. [24]
    M. Hanada, J. Maltz and L. Susskind, Deconfinement transition as black hole formation by the condensation of QCD strings, Phys. Rev. D 90 (2014) 105019 [arXiv:1405.1732] [INSPIRE].ADSGoogle Scholar
  25. [25]
    Y. Hidaka and R.D. Pisarski, Zero Point Energy of Renormalized Wilson Loops, Phys. Rev. D 80 (2009) 074504 [arXiv:0907.4609] [INSPIRE].ADSGoogle Scholar
  26. [26]
    S. Gupta, K. Huebner and O. Kaczmarek, Renormalized Polyakov loops in many representations, Phys. Rev. D 77 (2008) 034503 [arXiv:0711.2251] [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Mykkanen, M. Panero and K. Rummukainen, Casimir scaling and renormalization of Polyakov loops in large-N gauge theories, JHEP 05 (2012) 069 [arXiv:1202.2762] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Dumitru, J. Lenaghan and R.D. Pisarski, Deconfinement in matrix models about the Gross-Witten point, Phys. Rev. D 71 (2005) 074004 [hep-ph/0410294] [INSPIRE].
  29. [29]
    H. Nishimura, R.D. Pisarski and V.V. Skokov, Finite-temperature phase transitions of third and higher order in gauge theories at large N, Phys. Rev. D 97 (2018) 036014 [arXiv:1712.04465] [INSPIRE].ADSMathSciNetGoogle Scholar
  30. [30]
    B. de Wit, J. Hoppe and H. Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  33. [33]
    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].ADSMathSciNetGoogle Scholar
  34. [34]
    N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP 10 (2007) 097 [arXiv:0706.3517] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M.S. Costa, L. Greenspan, J. Penedones and J. Santos, Thermodynamics of the BMN matrix model at strong coupling, JHEP 03 (2015) 069 [arXiv:1411.5541] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    J. Maldacena and A. Milekhin, To gauge or not to gauge?, JHEP 04 (2018) 084 [arXiv:1802.00428] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  38. [38]
    E. Berkowitz, E. Rinaldi, M. Hanada, G. Ishiki, S. Shimasaki and P. Vranas, Precision lattice test of the gauge/gravity duality at large-N, Phys. Rev. D 94 (2016) 094501 [arXiv:1606.04951] [INSPIRE].ADSGoogle Scholar
  39. [39]
    E. Berkowitz, M. Hanada, E. Rinaldi and P. Vranas, Gauged And Ungauged: A Nonperturbative Test, JHEP 06 (2018) 124 [arXiv:1802.02985] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  40. [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, Class. Quant. Grav. 21 (2004) 5169 [hep-th/0406210] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP 12 (2010) 022 [arXiv:1008.4964] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    S. Catterall, R.G. Jha, D. Schaich and T. Wiseman, Testing holography using lattice super-Yang-Mills theory on a 2-torus, Phys. Rev. D 97 (2018) 086020 [arXiv:1709.07025] [INSPIRE].ADSMathSciNetGoogle Scholar
  43. [43]
    O.J.C. Dias, J.E. Santos and B. Way, Localised and nonuniform thermal states of super-Yang-Mills on a circle, JHEP 06 (2017) 029 [arXiv:1702.07718] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    T. Harmark, Small black holes on cylinders, Phys. Rev. D 69 (2004) 104015 [hep-th/0310259] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  45. [45]
    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].
  47. [47]
    S. Muroya, A. Nakamura, C. Nonaka and T. Takaishi, Lattice QCD at finite density: An introductory review, Prog. Theor. Phys. 110 (2003) 615 [hep-lat/0306031] [INSPIRE].
  48. [48]
    N. Jokela, A. Pönni and A. Vuorinen, Small black holes in global AdS spacetime, Phys. Rev. D 93 (2016) 086004 [arXiv:1508.00859] [INSPIRE].ADSGoogle Scholar
  49. [49]
    O.J. Dias, J.E. Santos and B. Way, Localised AdS 5 × S 5 Black Holes, Phys. Rev. Lett. 117 (2016) 151101 [arXiv:1605.04911] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    L.G. Yaffe, Large N phase transitions and the fate of small Schwarzschild-AdS black holes, Phys. Rev. D 97 (2018) 026010 [arXiv:1710.06455] [INSPIRE].ADSMathSciNetGoogle Scholar
  51. [51]
    D. Marolf, Microcanonical Path Integrals and the Holography of small Black Hole Interiors, JHEP 09 (2018) 114 [arXiv:1808.00394] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    D. Schaich, Progress and prospects of lattice supersymmetry, in 36th International Symposium on Lattice Field Theory (Lattice 2018) East Lansing, MI, United States, July 22–28, 2018, 2018, arXiv:1810.09282 [INSPIRE].
  53. [53]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    D. Berenstein, Negative specific heat from non-planar interactions and small black holes in AdS/CFT, arXiv:1810.07267 [INSPIRE].
  55. [55]
    D. Sumpter, Soccermatics: mathematical adventures in the beautiful game, Bloomsbury Publishing, (2016).Google Scholar
  56. [56]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.School of Physics and Astronomy, and STAG Research CentreUniversity of SouthamptonSouthamptonU.K.
  2. 2.Tomonaga Center for the History of the UniverseUniversity of TsukubaTsukubaJapan
  3. 3.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

Personalised recommendations