Abstract
We present a general treatment of the leading order dynamics of the collective modes of charged dilatonic p-brane solutions of (super) gravity theories in arbitrary backgrounds. To this end we employ the general strategy of the blackfold approach which is based on a long-wavelength derivative expansion around an exact or approximate solution of the (super)gravity equations of motion. The resulting collective mode equations are formulated as forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive them in full generality (including all possible asymptotic fluxes and dilaton profiles) in a far-zone analysis of the (super)gravity equations and in representative examples in a near-zone analysis. An independent treatment based on the study of external couplings in hydrostatic partition functions is also presented. Special emphasis is given to the forced collective mode equations that arise in type IIA/B and eleven-dimensional supergravities, where besides the standard Lorentz force couplings our analysis reveals additional couplings to the background, including terms that arise from Chern-Simons interactions. We also present a general overview of the blackfold approach and some of the key conceptual issues that arise when applied to arbitrary backgrounds.
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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].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
M. Rangamani, Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-Volume Effective Theory for Higher-Dimensional Black Holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of Blackfold Dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
J. Camps, R. Emparan and N. Haddad, Black Brane Viscosity and the Gregory-Laflamme Instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
R. Emparan, V.E. Hubeny and M. Rangamani, Effective hydrodynamics of black D3-branes, JHEP 06 (2013) 035 [arXiv:1303.3563] [INSPIRE].
S. Bhattacharyya, R. Loganayagam, S. Minwalla, S. Nampuri, S.P. Trivedi and S.R. Wadia, Forced Fluid Dynamics from Gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [INSPIRE].
J. Gath and A.V. Pedersen, Viscous asymptotically flat Reissner-Nordström black branes, JHEP 03 (2014) 059 [arXiv:1302.5480] [INSPIRE].
A. Di Dato, J. Gath and A.V. Pedersen, Probing the Hydrodynamic Limit of (Super)gravity, JHEP 04 (2015) 171 [arXiv:1501.05441] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The Phase Structure of Higher-Dimensional Black Rings and Black Holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black Rings in (Anti)-deSitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [INSPIRE].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black Rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, New Horizons for Black Holes and Branes, JHEP 04 (2010) 046 [arXiv:0912.2352] [INSPIRE].
G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Heating up the BIon, JHEP 06 (2011) 058 [arXiv:1012.1494] [INSPIRE].
M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional Rotating Charged Black Holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].
J. Armas and N.A. Obers, Blackfolds in (Anti)-de Sitter Backgrounds, Phys. Rev. D 83 (2011) 084039 [arXiv:1012.5081] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds in Supergravity and String Theory, JHEP 08 (2011) 154 [arXiv:1106.4428] [INSPIRE].
J. Armas, J. Camps, T. Harmark and N.A. Obers, The Young Modulus of Black Strings and the Fine Structure of Blackfolds, JHEP 02 (2012) 110 [arXiv:1110.4835] [INSPIRE].
J. Camps and R. Emparan, Derivation of the blackfold effective theory, JHEP 03 (2012) 038 [Erratum ibid. 1206 (2012) 155] [arXiv:1201.3506] [INSPIRE].
V. Niarchos and K. Siampos, M2-M5 blackfold funnels, JHEP 06 (2012) 175 [arXiv:1205.1535] [INSPIRE].
J. Armas, J. Gath and N.A. Obers, Black Branes as Piezoelectrics, Phys. Rev. Lett. 109 (2012) 241101 [arXiv:1209.2127] [INSPIRE].
J. Armas, J. Gath and N.A. Obers, Electroelasticity of Charged Black Branes, JHEP 10 (2013) 035 [arXiv:1307.0504] [INSPIRE].
J. Armas and M. Blau, Blackfolds, Plane Waves and Minimal Surfaces, JHEP 07 (2015) 156 [arXiv:1503.08834] [INSPIRE].
J. Armas and M. Blau, New Geometries for Black Hole Horizons, JHEP 07 (2015) 048 [arXiv:1504.01393] [INSPIRE].
J. Armas, T. Harmark, N.A. Obers, M. Orselli and A.V. Pedersen, Thermal Giant Gravitons, JHEP 11 (2012) 123 [arXiv:1207.2789] [INSPIRE].
J. Armas, N.A. Obers and A.V. Pedersen, Null-Wave Giant Gravitons from Thermal Spinning Brane Probes, JHEP 10 (2013) 109 [arXiv:1306.2633] [INSPIRE].
V. Niarchos, Open/closed string duality and relativistic fluids, Phys. Rev. D 94 (2016) 026009 [arXiv:1510.03438] [INSPIRE].
G. Grignani, T. Harmark, A. Marini and M. Orselli, Born-Infeld/gravity correspondence, Phys. Rev. D 94 (2016) 066009 [arXiv:1602.01640] [INSPIRE].
G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Thermodynamics of the hot BIon, Nucl. Phys. B 851 (2011) 462 [arXiv:1101.1297] [INSPIRE].
G. Grignani, T. Harmark, A. Marini and M. Orselli, Thermal DBI action for the D3-brane at weak and strong coupling, JHEP 03 (2014) 114 [arXiv:1311.3834] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [INSPIRE].
V. Niarchos, Supersymmetric Perturbations of the M5 brane, JHEP 05 (2014) 023 [arXiv:1402.4132] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
T. Harmark and N.A. Obers, Black holes on cylinders, JHEP 05 (2002) 032 [hep-th/0204047] [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].
W. Rindler, Relativity: Special, General, and Cosmological, Oxford University Press, (2001).
J. Bhattacharya, S. Bhattacharyya and S. Minwalla, Dissipative Superfluid dynamics from gravity, JHEP 04 (2011) 125 [arXiv:1101.3332] [INSPIRE].
E. Bergshoeff, R. Kallosh, T. Ortín, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8 - O8 domain walls, Class. Quant. Grav. 18(2001)3359 [hep-th/0103233] [INSPIRE].
G. Dall’Agata, K. Lechner and M. Tonin, D = 10, N = IIB supergravity., JHEP 07 (1998) 017 [hep-th/9806140] [INSPIRE].
I.A. Bandos, A.J. Nurmagambetov and D.P. Sorokin, Various faces of type IIA supergravity, Nucl. Phys. B 676 (2004) 189 [hep-th/0307153] [INSPIRE].
K. Becker, M. Becker and J. Schwarz, String Theory and M-Theory: A Modern Introduction, Cambridge University Press, (2006).
I.A. Bandos, N. Berkovits and D.P. Sorokin, Duality symmetric eleven-dimensional supergravity and its coupling to M-branes, Nucl. Phys. B 522 (1998) 214 [hep-th/9711055] [INSPIRE].
G.T. Horowitz and A. Strominger, Black strings and P-branes, Nucl. Phys. B 360 (1991) 197 [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [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, Supergravity and space-time noncommutative open string theory, JHEP 07 (2000) 043 [hep-th/0006023] [INSPIRE].
M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, arXiv:1511.03646 [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Topological σ-models & dissipative hydrodynamics, JHEP 04 (2016) 039 [arXiv:1511.07809] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J. Armas, How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes, JHEP 09 (2013) 073 [arXiv:1304.7773] [INSPIRE].
G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Thermal string probes in AdS and finite temperature Wilson loops, JHEP 06 (2012) 144 [arXiv:1201.4862] [INSPIRE].
V. Niarchos and K. Siampos, Entropy of the self-dual string soliton, JHEP 07 (2012) 134 [arXiv:1206.2935] [INSPIRE].
V. Niarchos and K. Siampos, The black M2-M5 ring intersection spins, PoS (Corfu2012) 088 [arXiv:1302.0854] [INSPIRE].
J. Armas and M. Blau, Black probes of Schrödinger spacetimes, JHEP 08 (2014) 140 [arXiv:1405.1301] [INSPIRE].
D. Giataganas and K. Goldstein, Tension of Confining Strings at Low Temperature, JHEP 02 (2015) 123 [arXiv:1411.4995] [INSPIRE].
I. Bena, M. Graña and N. Halmagyi, On the Existence of Meta-stable Vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [INSPIRE].
J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, (Anti-)Brane backreaction beyond perturbation theory, JHEP 02 (2012) 025 [arXiv:1111.2605] [INSPIRE].
I. Bena, J. Blabäck and D. Turton, Loop corrections to the antibrane potential, JHEP 07 (2016) 132 [arXiv:1602.05959] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and S. Massai, The backreaction of anti-D3 branes on the Klebanov-Strassler geometry, JHEP 06 (2013) 060 [arXiv:1106.6165] [INSPIRE].
I.R. Klebanov and S.S. Pufu, M-Branes and Metastable States, JHEP 08 (2011) 035 [arXiv:1006.3587] [INSPIRE].
I. Bena, G. Giecold and N. Halmagyi, The Backreaction of Anti-M2 Branes on a Warped Stenzel Space, JHEP 04 (2011) 120 [arXiv:1011.2195] [INSPIRE].
S. Massai, Metastable Vacua and the Backreacted Stenzel Geometry, JHEP 06 (2012) 059 [arXiv:1110.2513] [INSPIRE].
M. Gutperle and A. Strominger, Space-like branes, JHEP 04 (2002) 018 [hep-th/0202210] [INSPIRE].
A. Sen, Rolling tachyon, JHEP 04 (2002) 048 [hep-th/0203211] [INSPIRE].
D. Kutasov and V. Niarchos, Tachyon effective actions in open string theory, Nucl. Phys. B 666 (2003)56 [hep-th/0304045] [INSPIRE].
J. Armas, (Non)-Dissipative Hydrodynamics on Embedded Surfaces, JHEP 09 (2014) 047 [arXiv:1312.0597] [INSPIRE].
J. Armas and T. Harmark, Constraints on the effective fluid theory of stationary branes, JHEP 10 (2014) 063 [arXiv:1406.7813] [INSPIRE].
J. Armas, J. Bhattacharya and N. Kundu, Surface transport in plasma-balls, JHEP 06 (2016) 015 [arXiv:1512.08514] [INSPIRE].
J. Armas, N.A. Obers and M. Sanchioni, Gravitational Tension, Spacetime Pressure and Black Hole Volume, JHEP 09 (2016) 124 [arXiv:1512.09106] [INSPIRE].
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Armas, J., Gath, J., Niarchos, V. et al. Forced fluid dynamics from blackfolds in general supergravity backgrounds. J. High Energ. Phys. 2016, 154 (2016). https://doi.org/10.1007/JHEP10(2016)154
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DOI: https://doi.org/10.1007/JHEP10(2016)154