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)