Abstract
We construct the supergravity dual of the hot quark-gluon plasma in the mass-deformed \( \mathcal{N} \) = 4 Super-Yang-Mills theory (also known as \( \mathcal{N} \) = 1∗). The full ten-dimensional type IIB holographic dual is described by 20 functions of two variables, which we determine numerically, and it contains a black hole with S5 horizon topology. As we lower the temperature to around half of the mass of the chiral multiplets, we find evidence for (most likely a first-order) phase transition, which could lead either to one of the Polchinski-Strassler confining, screening, or oblique vacua with polarized branes, or to an intermediate phase corresponding to blackened polarized branes with an S2 ×S3 horizon topology. This phase transition is a feature that could in principle be seen by putting the theory on the lattice, and thus our result for the ratio of the chiral multiplet mass to the phase transition temperature, mc/T = 2.15467491205(6), constitutes the first prediction of string theory and AdS/CFT that could be independently checked via four-dimensional super-QCD lattice computation. We also construct the black-hole solution in certain five-dimensional gauged supergravity truncations and, without directly using uplift/reduction formulae, we find strong evidence that the five- and ten-dimensional solutions are the same. This indicates that five-dimensional gauged supergravity is powerful enough to capture the physics of the high-temperature deconfined phase of the Polchinski-Strassler quark-gluon plasma.
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G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett.87 (2001) 081601 [hep-th/0104066] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett.94 (2005) 111601 [hep-th/0405231] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev.D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys.B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
J. Polchinski and M.J. Strassler, The String dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
R.C. Myers, Dielectric branes, JHEP12 (1999) 022 [hep-th/9910053] [INSPIRE].
D.Z. Freedman and J.A. Minahan, Finite temperature effects in the supergravity dual of the N = 1∗gauge theory, JHEP01 (2001) 036 [hep-th/0007250] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113 (2005) 843 [hep-th/0412141] [INSPIRE].
E. Witten, Branes and the dynamics of QCD, Nucl. Phys.B 507 (1997) 658 [hep-th/9706109] [INSPIRE].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys.71 (1999) 983 [hep-th/9802067] [INSPIRE].
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].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP08 (2000) 052 [hep-th/0007191] [INSPIRE].
J.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys.247 (2004) 421 [hep-th/0205050] [INSPIRE].
C.N. Gowdigere, D. Nemeschansky and N.P. Warner, Supersymmetric solutions with fluxes from algebraic Killing spinors, Adv. Theor. Math. Phys.7 (2003) 787 [hep-th/0306097] [INSPIRE].
D. Nemeschansky and N.P. Warner, A Family of M-theory flows with four supersymmetries, hep-th/0403006 [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP10 (2004) 025 [hep-th/0409174] [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., pp. 233-270 (2012) [arXiv:1107.5513] [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].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The Supergravity dual of N = 1 superYang-Mills theory, Nucl. Phys.B 569 (2000) 451 [hep-th/9909047] [INSPIRE].
M. Petrini, H. Samtleben, S. Schmidt and K. Skenderis, The 10d Uplift of the GPPZ Solution, JHEP07 (2018) 026 [arXiv:1805.01919] [INSPIRE].
N. Bobev, F.F. Gautason, B.E. Niehoff and J. van Muiden, Uplifting GPPZ: a ten-dimensional dual of \( \mathcal{N} \) = 1∗, JHEP10 (2018) 058 [arXiv:1805.03623] [INSPIRE].
K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys.4 (2002) 627 [hep-th/0006066] [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, Consistent Type IIB Reductions to Maximal 5D Supergravity, Phys. Rev.D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys.B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys.B 447(1995) 95 [hep-th/9503121] [INSPIRE].
C. Vafa and E. Witten, A Strong coupling test of S duality, Nucl. Phys.B 431 (1994) 3 [hep-th/9408074] [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 Supergravity in Five-Dimensions, Phys. Lett.154B (1985) 268 [INSPIRE].
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 Supergravity, Nucl. Phys.B 259 (1985) 460 [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Compact and Noncompact Gauged Supergravity Theories in Five-Dimensions, Nucl. Phys.B 272 (1986) 598 [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev.D 62 (2000) 064028 [hep-th/0003286] [INSPIRE].
G.W. Gibbons and C.N. Pope, Consistent S 2Pauli reduction of six-dimensional chiral gauged Einstein-Maxwell supergravity, Nucl. Phys.B 697 (2004) 225 [hep-th/0307052] [INSPIRE].
B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP05 (2013) 077 [arXiv:1302.6219] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Nonlinear Kaluza-Klein theory for dual fields, Phys. Rev.D 88 (2013) 125002 [arXiv:1309.0266] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Testing the non-linear flux ansatz for maximal supergravity, Phys. Rev.D 87 (2013) 085038 [arXiv:1303.1013] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Generalised geometry from the ground up, JHEP02 (2014) 075 [arXiv:1307.8295] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions, Phys. Rev.D 89 (2014) 045009 [arXiv:1312.1061] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys.65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
K.A. Intriligator, Bonus symmetries of N = 4 superYang-Mills correlation functions via AdS duality, Nucl. Phys.B 551 (1999) 575 [hep-th/9811047] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys.B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP08 (2001) 041 [hep-th/0105276] [INSPIRE].
R.M. Wald, Dynamic and Thermodynamic Stability of Black Holes and Black Branes, Fundam. Theor. Phys.177 (2014) 229 [INSPIRE].
J.S. Schiffrin and R.M. Wald, Turning Point Instabilities for Relativistic Stars and Black Holes, Class. Quant. Grav.31 (2014) 035024 [arXiv:1310.5117] [INSPIRE].
J.H. Schwarz, Covariant Field Equations of Chiral N = 2 D = 10 Supergravity, Nucl. Phys.B 226 (1983) 269 [INSPIRE].
M. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev.D 65 (2002) 126005 [hep-th/0106014] [INSPIRE].
I. Bena, M. Graña, S. Kuperstein, P. Ntokos and M. Petrini, Fermionic and bosonic mass deformations of \( \mathcal{N} \) = 4 SYM and their bulk supergravity dual, JHEP05 (2016) 149 [arXiv:1512.00011] [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].
P. Figueras and T. Wiseman, On the existence of stationary Ricci solitons, Class. Quant. Grav.34 (2017) 145007 [arXiv:1610.06178] [INSPIRE].
Ó.J.C. Dias, G.T. Horowitz and J.E. Santos, Black holes with only one Killing field, JHEP07 (2011) 115 [arXiv:1105.4167] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Black holes with a single Killing vector field: black resonators, JHEP12 (2015) 171 [arXiv:1505.04793] [INSPIRE].
O.J.C. Dias, G.S. Hartnett, B.E. Niehoff and J.E. Santos, Energy in M-Theory and IIB, to be submitted (2018).
M. Taylor, Anomalies, counterterms and the N = 0 Polchinski-Strassler solutions, hep-th/0103162 [INSPIRE].
Ó.J.C. Dias, G.S. Hartnett, B.E. Niehoff and J.E. Santos, Mass-deformed M2 branes in Stenzel space, JHEP11 (2017) 105 [arXiv:1704.02323] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett.70 (1993) 2837 [hep-th/9301052] [INSPIRE].
T. Wiseman, Static axisymmetric vacuum solutions and nonuniform black strings, Class. Quant. Grav.20 (2003) 1137 [hep-th/0209051] [INSPIRE].
M. Kalisch and M. Ansorg, Highly Deformed Non-uniform Black Strings in Six Dimensions, in Proceedings, 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG14), (in 4 volumes), Rome, Italy, 12-18 July 2015, vol. 2, pp. 1799-1804 (2017) [DOI:10.1142/9789813226609 0185] [arXiv:1509.03083] [INSPIRE].
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].
Ó.J.C. Dias, J.E. Santos and B. Way, Rings, Ripples and Rotation: Connecting Black Holes to Black Rings, JHEP07 (2014) 045 [arXiv:1402.6345] [INSPIRE].
R. Emparan, P. Figueras and M. Martinez, Bumpy black holes, JHEP12 (2014) 072 [arXiv:1410.4764] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Lumpy AdS 5× S 5black holes and black belts, JHEP04 (2015) 060 [arXiv:1501.06574] [INSPIRE].
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Bena, I., Dias, Ó.J., Hartnett, G.S. et al. Holographic dual of hot Polchinski-Strassler quark-gluon plasma. J. High Energ. Phys. 2019, 33 (2019). https://doi.org/10.1007/JHEP09(2019)033
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DOI: https://doi.org/10.1007/JHEP09(2019)033