Abstract
At low energies or temperatures, maximally supersymmetric Yang-Mills theory on \( {\mathbb{R}}^{(t)}\times {S}^1 \) with large N gauge group SU(N ) and strong t’Hooft coupling is conjectured to be dual to the low energy dynamics of a collection of D0-branes on a circle. We construct thermal states in the gravitational side of the correspondence where we find a first-order phase transition between states that are uniform on the S 1 and states that are localised on it. When compared with lattice computations that are now available, these critical values provide the first instance where a first-order phase transition is tested on both sides of gauge/gravity duality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
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].
N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling, Phys. Rev. Lett. 104 (2010) 211601 [arXiv:0906.4240] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, arXiv:1608.07294 [INSPIRE].
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].
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].
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].
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].
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].
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].
S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP 04 (2010) 077 [arXiv:0909.4947] [INSPIRE].
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].
M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Holographic description of quantum black hole on a computer, Science 344 (2014) 882 [arXiv:1311.5607] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
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].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [INSPIRE].
R. Gregory and R. Laflamme, Evidence for stability of extremal black p-branes, Phys. Rev. D 51 (1995) 305 [hep-th/9410050] [INSPIRE].
L. Susskind, Matrix theory black holes and the Gross-Witten transition, hep-th/9805115 [INSPIRE].
J.L.F. Barbon, I.I. Kogan and E. Rabinovici, On stringy thresholds in SYM/AdS thermodynamics, Nucl. Phys. B 544 (1999) 104 [hep-th/9809033] [INSPIRE].
M. Li, E.J. Martinec and V. Sahakian, Black holes and the SYM phase diagram, Phys. Rev. D 59 (1999) 044035 [hep-th/9809061] [INSPIRE].
L. Fidkowski and S. Shenker, D-brane instability as a large-N phase transition, hep-th/0406086 [INSPIRE].
E. Martinec, The d-star and its decays, (1998) http://online.kitp.ucsb.edu/online/strings98/martinec/.
Ó.J.C. Dias, J.E. Santos and B. Way, Lumpy AdS5 × S5 black holes and black belts, JHEP 04 (2015) 060 [arXiv:1501.06574] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Localised AdS5 × S5 Black Holes, Phys. Rev. Lett. 117 (2016) 151101 [arXiv:1605.04911] [INSPIRE].
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].
T. Azeyanagi, M. Hanada, T. Hirata and H. Shimada, On the shape of a D-brane bound state and its topology change, JHEP 03 (2009) 121 [arXiv:0901.4073] [INSPIRE].
M. Hanada and I. Kanamori, Lattice study of two-dimensional N = (2, 2) super Yang-Mills at large-N , Phys. Rev. D 80 (2009) 065014 [arXiv:0907.4966] [INSPIRE].
M. Hanada, S. Matsuura and F. Sugino, Two-dimensional lattice for four-dimensional N = 4 supersymmetric Yang-Mills, Prog. Theor. Phys. 126 (2011) 597 [arXiv:1004.5513] [INSPIRE].
M. Hanada, A proposal of a fine tuning free formulation of 4d N = 4 super Yang-Mills, JHEP 11 (2010) 112 [arXiv:1009.0901] [INSPIRE].
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].
M. Hanada and P. Romatschke, Lattice Simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d, arXiv:1612.06395 [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, M. Van Raamsdonk and T. Wiseman, The Phase structure of low dimensional large-N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [INSPIRE].
E. Giguère and D. Kadoh, Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice, JHEP 05 (2015) 082 [arXiv:1503.04416] [INSPIRE].
D. Kadoh, Precision test of the gauge/gravity duality in two-dimensional N = (8, 8) SYM, PoS(LATTICE2016)033 [arXiv:1702.01615] [INSPIRE].
B. Kol, Topology change in general relativity and the black hole black string transition, JHEP 10 (2005) 049 [hep-th/0206220] [INSPIRE].
T. Wiseman, Static axisymmetric vacuum solutions and nonuniform black strings, Class. Quant. Grav. 20 (2003) 1137 [hep-th/0209051] [INSPIRE].
B. Kol and T. Wiseman, Evidence that highly nonuniform black strings have a conical waist, Class. Quant. Grav. 20 (2003) 3493 [hep-th/0304070] [INSPIRE].
T. Harmark, Small black holes on cylinders, Phys. Rev. D 69 (2004) 104015 [hep-th/0310259] [INSPIRE].
D. Gorbonos and B. Kol, A dialogue of multipoles: Matched asymptotic expansion for caged black holes, JHEP 06 (2004) 053 [hep-th/0406002] [INSPIRE].
T. Harmark and N.A. Obers, New phases of near-extremal branes on a circle, JHEP 09 (2004) 022 [hep-th/0407094] [INSPIRE].
V. Asnin, B. Kol and M. Smolkin, Analytic evidence for continuous self similarity of the critical merger solution, Class. Quant. Grav. 23 (2006) 6805 [hep-th/0607129] [INSPIRE].
T. Harmark and N.A. Obers, Black holes on cylinders, JHEP 05 (2002) 032 [hep-th/0204047] [INSPIRE].
T. Wiseman, From black strings to black holes, Class. Quant. Grav. 20 (2003) 1177 [hep-th/0211028] [INSPIRE].
H. Kudoh and T. Wiseman, Properties of Kaluza-Klein black holes, Prog. Theor. Phys. 111 (2004) 475 [hep-th/0310104] [INSPIRE].
H. Kudoh and T. Wiseman, Connecting black holes and black strings, Phys. Rev. Lett. 94 (2005) 161102 [hep-th/0409111] [INSPIRE].
E. Sorkin, Non-uniform black strings in various dimensions, Phys. Rev. D 74 (2006) 104027 [gr-qc/0608115] [INSPIRE].
B. Kleihaus, J. Kunz and E. Radu, New nonuniform black string solutions, JHEP 06 (2006) 016 [hep-th/0603119] [INSPIRE].
T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav. 24 (2007) R1 [hep-th/0701022] [INSPIRE].
Ó.J.C. Dias, T. Harmark, R.C. Myers and N.A. Obers, Multi-black hole configurations on the cylinder, Phys. Rev. D 76 (2007) 104025 [arXiv:0706.3645] [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A New approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
T. Wiseman, Numerical construction of static and stationary black holes, in Black Holes in Higher Dimensions, G.T. Horowitz ed., Cambridge University Press (2012) [arXiv:1107.5513] [INSPIRE].
P. Figueras, K. Murata and H.S. Reall, Stable non-uniform black strings below the critical dimension, JHEP 11 (2012) 071 [arXiv:1209.1981] [INSPIRE].
G.T. Horowitz et al., Black Holes in Higher Dimensions, Cambridge University Press (2012).
M. Kalisch and M. Ansorg, Pseudo-spectral construction of non-uniform black string solutions in five and six spacetime dimensions, Class. Quant. Grav. 33 (2016) 215005 [arXiv:1607.03099] [INSPIRE].
E. Sorkin, B. Kol and T. Piran, Caged black holes: Black holes in compactified space-times. 2. 5-D numerical implementation, Phys. Rev. D 69 (2004) 064032 [hep-th/0310096] [INSPIRE].
T. Harmark and N.A. Obers, Thermodynamics of spinning branes and their dual field theories, JHEP 01 (2000) 008 [hep-th/9910036] [INSPIRE].
T. Harmark, V. Niarchos and N.A. Obers, Instabilities of near-extremal smeared branes and the correlated stability conjecture, JHEP 10 (2005) 045 [hep-th/0509011] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir Energy in Curved Space and its Supersymmetric Counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].
T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
B. Kol, E. Sorkin and T. Piran, Caged black holes: Black holes in compactified space-times. 1. Theory, Phys. Rev. D 69 (2004) 064031 [hep-th/0309190] [INSPIRE].
T. Harmark and N.A. Obers, New phase diagram for black holes and strings on cylinders, Class. Quant. Grav. 21 (2004) 1709 [hep-th/0309116] [INSPIRE].
P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav. 28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
N. Kawahara, J. Nishimura and S. Takeuchi, High temperature expansion in supersymmetric matrix quantum mechanics, JHEP 12 (2007) 103 [arXiv:0710.2188] [INSPIRE].
G. Mandal, M. Mahato and T. Morita, Phases of one dimensional large-N gauge theory in a 1/D expansion, JHEP 02 (2010) 034 [arXiv:0910.4526] [INSPIRE].
T. Azuma, T. Morita and S. Takeuchi, Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities, Phys. Rev. Lett. 113 (2014) 091603 [arXiv:1403.7764] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, to be published (2017).
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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1702.07718
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Dias, Ó.J.C., Santos, J.E. & Way, B. Localised and nonuniform thermal states of super-Yang-Mills on a circle. J. High Energ. Phys. 2017, 29 (2017). https://doi.org/10.1007/JHEP06(2017)029
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2017)029