Hydrodynamics of Rcharged D1branes
 Justin R. David,
 Manavendra Mahato,
 Somyadip Thakur,
 Spenta R. Wadia
 … show all 4 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We study the hydrodynamic properties of strongly coupled SU(N) YangMills theory of the D1brane at finite temperature and at a nonzero density of Rcharge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an EinsteinMaxwelldilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the Rcharges of the D1brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/π4. The thermal conductivity and bulk viscosity obey a relationship similar to the WiedemannFranz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1brane theory are related to that of the M2brane by an overall proportionality constant which sets the dimensions.
 Kovtun, P, Son, DT, Starinets, AO (2003) Holography and hydrodynamics: Diffusion on stretched horizons. JHEP 10: pp. 064 CrossRef
 Buchel, A, Liu, JT (2004) Universality of the shear viscosity in supergravity. Phys. Rev. Lett. 93: pp. 090602 CrossRef
 Rangamani, M (2009) Gravity & hydrodynamics: Lectures on the fluidgravity correspondence. Class. Quant. Grav. 26: pp. 224003 CrossRef
 Boonstra, HJ, Skenderis, K, Townsend, PK (1999) The domain wall/QFT correspondence. JHEP 01: pp. 003 CrossRef
 Itzhaki, N, Maldacena, JM, Sonnenschein, J, Yankielowicz, S (1998) Supergravity and the largeN limit of theories with sixteen supercharges. Phys. Rev. D 58: pp. 046004
 Mas, J, Tarrio, J (2007) Hydrodynamics from the Dpbrane. JHEP 05: pp. 036 CrossRef
 David, JR, Mahato, M, Wadia, SR (2009) Hydrodynamics from the D1brane. JHEP 04: pp. 042 CrossRef
 Kanitscheider, I, Skenderis, K, Taylor, M (2008) Precision holography for nonconformal branes. JHEP 09: pp. 094 CrossRef
 Buchel, A (2008) Bulk viscosity of gauge theory plasma at strong coupling. Phys. Lett. B 663: pp. 286 CrossRef
 Deshpande, VV, Bockrath, M, Glazman, LI, Yacoby, A (2010) Electron liquids and solids in one dimension. Nature 464: pp. 209 CrossRef
 Maity, D, Sarkar, S, Sircar, N, Sathiapalan, B, Shankar, R (2010) Properties of CFT s dual to Charged BTZ blackhole. Nucl. Phys. B 839: pp. 526 CrossRef
 Hung, LY, Sinha, A (2010) Holographic quantum liquids in 1 + 1 dimensions. JHEP 01: pp. 114 CrossRef
 Herzog, CP (2002) The hydrodynamics of Mtheory. JHEP 12: pp. 026 CrossRef
 Herzog, CP (2003) The sound of Mtheory. Phys. Rev. D 68: pp. 024013
 Saremi, O (2006) The viscosity bound conjecture and hydrodynamics of M2brane theory at finite chemical potential. JHEP 10: pp. 083 CrossRef
 Hartnoll, SA, Herzog, CP (2007) Ohm’s Law at strong coupling: S duality and the cyclotron resonance. Phys. Rev. D 76: pp. 106012
 Herzog, CP, Kovtun, P, Sachdev, S, Son, DT (2007) Quantum critical transport, duality and Mtheory. Phys. Rev. D 75: pp. 085020
 Son, DT, Starinets, AO (2006) Hydrodynamics of Rcharged black holes. JHEP 03: pp. 052 CrossRef
 Harmark, T, Obers, NA (2000) Thermodynamics of spinning branes and their dual field theories. JHEP 01: pp. 008 CrossRef
 Cvetič, M, Lü, H, Pope, CN (2000) Consistent KaluzaKlein sphere reductions. Phys. Rev. D 62: pp. 064028
 Kovtun, PK, Starinets, AO (2005) Quasinormal modes and holography. Phys. Rev. D 72: pp. 086009
 Son, DT, Starinets, AO (2002) Minkowskispace correlators in AdS/CFT correspondence: Recipe and applications. JHEP 09: pp. 042 CrossRef
 Herzog, CP, Son, DT (2003) SchwingerKeldysh propagators from AdS/CFT correspondence. JHEP 03: pp. 046 CrossRef
 Banerjee, N, Dutta, S (2010) Nonlinear hydrodynamics from flow of retarded Green’s function. JHEP 08: pp. 041 CrossRef
 I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, arXiv:1006.1902[SPIRES].
 Iqbal, N, Liu, H (2009) Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm. Phys. Rev. D 79: pp. 025023
 Jain, S (2010) Universal thermal and electrical conductivity from holography. JHEP 11: pp. 092 CrossRef
 Policastro, G, Son, DT, Starinets, AO (2002) From AdS/CFT correspondence to hydrodynamics. II: Sound waves. JHEP 12: pp. 054 CrossRef
 Peet, AW, Polchinski, J (1999) UV/IR relations in AdS dynamics. Phys. Rev. D 59: pp. 065011
 Mateos, D, Myers, RC, Thomson, RM (2007) Thermodynamics of the brane. JHEP 05: pp. 067 CrossRef
 Kanitscheider, I, Skenderis, K (2009) Universal hydrodynamics of nonconformal branes. JHEP 04: pp. 062 CrossRef
 Bjorken, JD (1983) Highly relativistic nucleusnucleus collisions: the central rapidity region. Phys. Rev. D 27: pp. 140
 Kane, CL, Mele, EJ (1997) Size, shape, and low energy electronic structure of carbon nanotubes. Phys. Rev. Lett. 78: pp. 1932 CrossRef
 Brey, L, Fertig, HA (2006) Electronic states of graphene nanoribbons studied with the dirac equation. Phys. Rev. B 73: pp. 235411
 Damle, K, Sachdev, S (1998) Spin dynamics and transport in gapped onedimensional heisenberg antiferromagnets at nonzero temperatures. Phys. Rev. B 57: pp. 8307
 Buragohain, C, Sachdev, S (1999) Intermediatetemperature dynamics of onedimensional heisenberg antiferromagnets. Phys. Rev. B 59: pp. 9285
 Barrau, S, Demont, P, Peigney, A, Laurent, C, Lacabanne, C (2003) DC and AC conductivity of carbon nanotubespolyepoxy composites. Macromolecules 36: pp. 5187 CrossRef
 Hartnoll, SA, Kovtun, P (2007) Hall conductivity from dyonic black holes. Phys. Rev. D 76: pp. 066001
 Title
 Hydrodynamics of Rcharged D1branes
 Journal

Journal of High Energy Physics
2011:14
 Online Date
 January 2011
 DOI
 10.1007/JHEP01(2011)014
 Online ISSN
 10298479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Gaugegravity correspondence
 Dbranes
 Holography and condensed matter physics (AdS/CMT)
 Industry Sectors
 Authors

 Justin R. David ^{(1)}
 Manavendra Mahato ^{(2)}
 Somyadip Thakur ^{(1)}
 Spenta R. Wadia ^{(2)} ^{(3)}
 Author Affiliations

 1. Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore, 560012, India
 2. Department of Theoretical Physics, TIFR, HomiBhabha Road, Mumbai, 400005, India
 3. International Centre for Theoretical Sciences, TIFR, HomiBhabha Road, Mumbai, 400005, India