Submatrix deconfinement and small black holes in AdS

Journal of High Energy Physics, Sep 2018

Abstract Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order N 2 at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies 1 ≪ E ≪ N 2 in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a U(M) subgroup of U(N), with M ≪ N have an excitation energy of order M 2 and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in AdS are discussed.

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Submatrix deconfinement and small black holes in AdS

Journal of High Energy Physics September 2018, 2018:54 | Cite as Submatrix deconfinement and small black holes in AdS AuthorsAuthors and affiliations David Berenstein Open Access Regular Article - Theoretical Physics First Online: 11 September 2018 Received: 26 June 2018 Accepted: 14 August 2018 21 Downloads Abstract Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order N 2 at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies 1 ≪ E ≪ N 2 in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a U(M) subgroup of U(N), with M ≪ N have an excitation energy of order M 2 and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in AdS are discussed. Keywords Confinement AdS-CFT Correspondence Black Holes in String Theory Matrix Models  ArXiv ePrint: 1806.05729 Download to read the full article text 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] 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 [2] R. Hagedorn, Hadronic matter near the boiling point, Nuovo Cim. A 56 (1968) 1027 [INSPIRE]. [3] O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar [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] S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [6] C.T. Asplund and D. Berenstein, Small AdS black holes from SYM, Phys. Lett. B 673 (2009) 264 [arXiv:0809.0712] [INSPIRE]. [7] 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]. [8] 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]. [9] D. Berenstein, Large N BPS states and emergent quantum gravity, JHEP 01 (2006) 125 [hep-th/0507203] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [10] D. Berenstein, Extremal chiral ring states in the AdS/CFT correspondence are described by free fermions for a generalized oscillator algebra, Phys. Rev. D 92 (2015) 046006 [arXiv:1504.05389] [INSPIRE]. [11] V. Balasubramanian, D. Berenstein, B. Feng and M.-x. Huang, D-branes in Yang-Mills theory and emergent gauge symmetry, JHEP 03 (2005) 006 [hep-th/0411205] [INSPIRE].ADSMathSciNetGoogle Scholar [12] R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons — with Strings Attached (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].MathSciNetCrossRefGoogle Scholar [13] D. Berenstein, A Matrix model for a quantum Hall droplet with manifest particle-hole symmetry, Phys. Rev. D 71 (2005) 085001 [hep-th/0409115] [INSPIRE]. [14] R. Bhattacharyya, S. Collins and R. de Mello Koch, Exact Multi-Matrix Correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [15] P. Mattioli and S. Ramgoolam, Permutation Centralizer Algebras and Multi-Matrix Invariants, Phys. Rev. D 93 (2016) 065040 [arXiv:1601.06086] [INSPIRE]. [16] S. Ramgoolam, Permutations and the combinatorics of gauge invariants for general N, PoS(CORFU2015)107 [arXiv:1605.00843] [INSPIRE]. [17] J. Pasukonis and S. Ramgoolam, Quivers as Calculators: Counting, Correlators and Riemann Surfaces, JHEP 04 (2013) 094 [arXiv:1301.1980] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [18] V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [19] S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [INSPIRE]. [20] J. McGreevy, L. Susskind and N. Toumbas, Invas (...truncated)


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David Berenstein. Submatrix deconfinement and small black holes in AdS, Journal of High Energy Physics, 2018, pp. 54, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)054