Abstract
Quasi-topological gravity is a new gravitational theory including curvaturecubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be dual to the large N c limit of some non-supersymmetric but conformal gauge theory. We establish various elements of the AdS/CFT dictionary for this duality. This allows us to infer physical constraints on the couplings in the gravitational theory. Further we use holography to investigate hydrodynamic aspects of the dual gauge theory. In particular, we find that the minimum value of the shear-viscosity-to-entropy-density ratio for this model is η/s ≃ 0.4140/(4π).
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J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
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] [SPIRES].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
D.T. Son and A.O. Starinets, Viscosity, black holes and quantum field theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].
A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [hep-th/0406264] [SPIRES].
A. Buchel, Resolving disagreement for eta/s in a CFT plasma at finite coupling, Nucl. Phys. B 803 (2008) 166 [arXiv:0805.2683] [SPIRES].
Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to eta/s, Phys. Rev. D 79 (2009) 041901 [arXiv:0806.2156] [SPIRES].
A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at finite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837] [SPIRES].
A. Buchel, R.C. Myers and A. Sinha, Beyond η/s = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [SPIRES].
A. Sinha and R.C. Myers, The viscosity bound in string theory, Nucl. Phys. A 830 (2009) 295c–298c [arXiv:0907.4798] [SPIRES].
D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [SPIRES].
D.M. Hofman, Higher derivative gravity, causality and positivity of energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [SPIRES].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [SPIRES].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [SPIRES].
A. Buchel and R.C. Myers, Causality of holographic hydrodynamics, JHEP 08 (2009) 016 [arXiv:0906.2922] [SPIRES].
J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7/CFT 6 , Gauss-Bonnet gravity and viscosity bound, JHEP 03 (2010) 087 [arXiv:0910.5347] [SPIRES].
X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [SPIRES]
A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [SPIRES].
X.-H. Ge and S.-J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527] [SPIRES].
R.-G. Cai, Z.-Y. Nie and Y.-W. Sun, Shear viscosity from effective couplings of gravitons, Phys. Rev. D 78 (2008) 126007 [arXiv:0811.1665] [SPIRES].
R.-G. Cai, Z.-Y. Nie, N. Ohta and Y.-W. Sun, Shear viscosity from Gauss-Bonnet gravity with a dilaton coupling, Phys. Rev. D 79 (2009) 066004 [arXiv:0901.1421] [SPIRES].
M.J. Duff, Observations on conformal anomalies, Nucl. Phys. B 125 (1977) 334 [SPIRES].
S. Nojiri and S.D. Odintsov, On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence, Int. J. Mod. Phys. A 15 (2000) 413 [hep-th/9903033] [SPIRES].
M. Blau, K.S. Narain and E. Gava, On subleading contributions to the AdS/CFT trace anomaly, JHEP 09 (1999) 018 [hep-th/9904179] [SPIRES].
X.-H. Ge, S.-J. Sin, S.-F. Wu and G.-H. Yang, Shear viscosity and instability from third order Lovelock gravity, Phys. Rev. D 80 (2009) 104019 [arXiv:0905.2675] [SPIRES].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic lovelock gravities and black holes, JHEP 06 (2010) 008 [arXiv:0912.1877] [SPIRES].
X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944] [SPIRES].
F.-W. Shu, The quantum viscosity bound in lovelock gravity, Phys. Lett. B 685 (2010) 325 [arXiv:0910.0607] [SPIRES].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, arXiv:1006.1263 [SPIRES].
R.C. Myers and A. Sinha, Anomalies, central charges and holography, to appear.
C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267] [SPIRES].
A. Schwimmer and S. Theisen, Universal features of holographic anomalies, JHEP 10 (2003) 001 [hep-th/0309064] [SPIRES].
A. Schwimmer and S. Theisen, Entanglement entropy, trace anomalies and holography, Nucl. Phys. B 801 (2008) 1 [arXiv:0802.1017] [SPIRES].
R.C. Myers and B. Robinson, Black Holes in Quasi-topological Gravity, arXiv:1003.5357 [SPIRES].
I. Fouxon, G. Betschart and J.D. Bekenstein, The bound on viscosity and the generalized second law of thermodynamics, Phys. Rev. D 77 (2008) 024016 [arXiv:0710.1429] [SPIRES].
H. Liu and A.A. Tseytlin, D = 4 super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083] [SPIRES].
G. Arutyunov and S. Frolov, Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 026004 [hep-th/9901121] [SPIRES].
A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [SPIRES].
I. Gullu, T.C. Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [SPIRES].
J. Oliva and S. Ray, A new cubic theory of gravity in five dimensions: Black hole, Birkhoff’s theorem and C-function, arXiv:1003.4773 [SPIRES].
J. Oliva and S. Ray, A classification of six derivative lagrangians of gravity and static spherically symmetric solutions, arXiv:1004.0737 [SPIRES].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [SPIRES].
M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [SPIRES].
V.K. Dobrev, E.K. Khristova, V.B. Petkova and D.B. Stamenov, Conformal covariant operator product expansion of two spin 1/2 fields, Bulg. J. Phys. 1 (1974) 42.
V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova and I.T. Todorov, Harmonic analysis on the N-dimensional Lorentz group and its application to conformal quantum field theory, in Lecture Notes in Physics 63 (1977) 280 [SPIRES].
I.T. Todorov, M.C. Mintchev and V.B. Petkova, Conformal invariance in quantum field theory, Sc. Norm. Sup., Pisa Italy (1978), pg. 273 [SPIRES].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Ann. Phys. 231 (1994) 311 [hep-th/9307010] [SPIRES].
D. Anselmi, M.T. Grisaru and A. Johansen, A critical behaviour of anomalous currents, electric-magnetic universality and CFT 4, Nucl. Phys. B 491 (1997) 221 [hep-th/9601023] [SPIRES].
N. Banerjee and S. Dutta, Shear viscosity to entropy density ratio in six derivative gravity, JHEP 07 (2009) 024 [arXiv:0903.3925] [SPIRES].
J. Erdmenger and H. Osborn, Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [SPIRES].
S.S. Gubser and I.R. Klebanov, Absorption by branes and Schwinger terms in the world volume theory, Phys. Lett. B 413 (1997) 41 [hep-th/9708005] [SPIRES].
.T. Horowitz and N. Itzhaki, Black holes, shock waves and causality in the AdS/CFT correspondence, JHEP 02 (1999) 010 [hep-th/9901012] [SPIRES].
G.T. Horowitz and A.R. Steif, Space-time singularities in string theory, Phys. Rev. Lett. 64 (1990) 260 [SPIRES].
J.I. Latorre and H. Osborn, Modified weak energy condition for the energy momentum tensor in quantum field theory, Nucl. Phys. B 511 (1998) 737 [hep-th/9703196] [SPIRES].
L. Brillouin, Wave propagation and group velocity, Academic Press (1960).
R. Fox, C.G. Kuper and S.G. Lipson, Faster-than-light group velocities and causality violation, Proc. Roy. Soc. Lond. A 316 (1970) 515.
E. Krotscheck and W. Kundt, Causality criteria, Commun. Math. Phys. 60 (1978) 171.
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [SPIRES].
N. Banerjee and S. Dutta, Higher derivative corrections to shear viscosity from graviton’s effective coupling, JHEP 03 (2009) 116 [arXiv:0901.3848] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [SPIRES].
M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [SPIRES].
R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [SPIRES].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [SPIRES].
K.M. Case, Singular potentials, Phys. Rev. 80 (1950) 797.
V. de Alfaro, S. Fubini and G. Furlan, Conformal invariance in quantum mechanics, Nuovo Cim. A 34 (1976) 569 [SPIRES].
S.R. Beane et al., Singular potentials and limit cycles, Phys. Rev. A 64 (2001) 042103 [quant-ph/0010073] [SPIRES].
L.D. Landau, E.M. Lifshitz, Quantum mechanics: non-relativistic theory, Pergamon Press (1977).
M. Kulaxizi and A. Parnachev, Supersymmetry constraints in holographic gravities, arXiv:0912.4244 [SPIRES].
T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196 (1982) 189 [SPIRES].
F. Sannino, Dynamical Stabilization of the Fermi scale: phase diagram of strongly coupled theories for (Minimal) walking technicolor and unparticles, arXiv:0804.0182 [SPIRES].
F. Sannino, Phase Diagrams of Strongly Interacting Theories, arXiv:1003.0289 [SPIRES].
F. Sannino, Conformal dynamics for TeV physics and cosmology, arXiv:0911.0931 [SPIRES].
E. Poppitz and M. Ünsal, Conformality or confinement: (IR)relevance of topological excitations, JHEP 09 (2009) 050 [arXiv:0906.5156] [SPIRES].
E. Poppitz and M. Ünsal, Conformality or confinement (II): one-flavor CFTs and mixed-representation QCD, JHEP 12 (2009) 011 [arXiv:0910.1245] [SPIRES].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [SPIRES].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [SPIRES].
M. Jarvinen and F. Sannino, Holographic conformal window - a bottom up approach, JHEP 05 (2010) 041 [arXiv:0911.2462] [SPIRES].
F. Bigazzi, R. Casero, A.L. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [SPIRES].
R. Brustein and A.J.M. Medved, The ratio of shear viscosity to entropy density in generalized theories of gravity, Phys. Rev. D 79 (2009) 021901 [arXiv:0808.3498] [SPIRES].
M. Paulos, Lovelock theories, holography and the fate of the viscosity bound.,unpublished.
X.O. Camanho, J.D. Edelstein and M. Paulos, in preparation.
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [SPIRES].
D. Lovelock, Divergence-free tensorial concomitants, Aequationes Math. 4 (1970) 127.
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [SPIRES].
M. Henneaux, C. Teitelboim and J. Zanelli, Quantum mechanics for multivalued Hamiltonians, Phys. Rev. A 36 (1987) 4417 [SPIRES].
C. Teitelboim and J. Zanelli, Dimensionally continued topological gravitation theory in Hamiltonian form, Class. Quantum Grav. 4 (1987) L125.
J. Alanen and K. Kajantie, Thermodynamics of a field theory with infrared fixed point from gauge/gravity duality, Phys. Rev. D 81 (2010) 046003 [arXiv:0912.4128] [SPIRES].
J. Alanen, K. Kajantie and K. Tuominen, Thermodynamics of quasi conformal theories from gauge/gravity duality, arXiv:1003.5499 [SPIRES].
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ArXiv ePrint: arXiv:1004.2055
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Myers, R.C., Paulos, M.F. & Sinha, A. Holographic studies of quasi-topological gravity. J. High Energ. Phys. 2010, 35 (2010). https://doi.org/10.1007/JHEP08(2010)035
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DOI: https://doi.org/10.1007/JHEP08(2010)035