Hydrodynamics of R-charged D1-branes
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We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane 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 R-charges of the D1-brane. 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 Wiedemann-Franz 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 D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.
- P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [SPIRES]. CrossRef
- A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES]. CrossRef
- M. Rangamani, Gravity & hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [SPIRES]. CrossRef
- H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [SPIRES]. CrossRef
- 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] [SPIRES].
- J. Mas and J. Tarrio, Hydrodynamics from the Dp-brane, JHEP 05 (2007) 036 [hep-th/0703093] [SPIRES]. CrossRef
- J.R. David, M. Mahato and S.R. Wadia, Hydrodynamics from the D1-brane, JHEP 04 (2009) 042 [arXiv:0901.2013] [SPIRES]. CrossRef
- I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [SPIRES]. CrossRef
- A. Buchel, Bulk viscosity of gauge theory plasma at strong coupling, Phys. Lett. B 663 (2008) 286 [arXiv:0708.3459] [SPIRES]. CrossRef
- V.V. Deshpande, M. Bockrath, L.I. Glazman and A. Yacoby, Electron liquids and solids in one dimension, Nature 464 (2010) 209. CrossRef
- D. Maity, S. Sarkar, N. Sircar, B. Sathiapalan and R. Shankar, Properties of CFT s dual to Charged BTZ black-hole, Nucl. Phys. B 839 (2010) 526 [arXiv:0909.4051] [SPIRES]. CrossRef
- L.-Y. Hung and A. Sinha, Holographic quantum liquids in 1 + 1 dimensions, JHEP 01 (2010) 114 [arXiv:0909.3526] [SPIRES]. CrossRef
- C.P. Herzog, The hydrodynamics of M-theory, JHEP 12 (2002) 026 [hep-th/0210126] [SPIRES]. CrossRef
- C.P. Herzog, The sound of M-theory, Phys. Rev. D 68 (2003) 024013 [hep-th/0302086] [SPIRES].
- O. Saremi, The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical potential, JHEP 10 (2006) 083 [hep-th/0601159] [SPIRES]. CrossRef
- S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [SPIRES].
- C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [SPIRES].
- D.T. Son and A.O. Starinets, Hydrodynamics of R-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [SPIRES]. CrossRef
- T. Harmark and N.A. Obers, Thermodynamics of spinning branes and their dual field theories, JHEP 01 (2000) 008 [hep-th/9910036] [SPIRES]. CrossRef
- M. Cvetič, H. Lü and C.N. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev. D 62 (2000) 064028 [hep-th/0003286] [SPIRES].
- P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [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]. CrossRef
- C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES]. CrossRef
- N. Banerjee and S. Dutta, Nonlinear hydrodynamics from flow of retarded Green’s function, JHEP 08 (2010) 041 [arXiv:1005.2367] [SPIRES]. CrossRef
- I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, arXiv:1006.1902[SPIRES].
- 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].
- S. Jain, Universal thermal and electrical conductivity from holography, JHEP 11 (2010) 092 [arXiv:1008.2944] [SPIRES]. CrossRef
- G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. II: Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [SPIRES]. CrossRef
- A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev. D 59 (1999) 065011 [hep-th/9809022] [SPIRES].
- D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [SPIRES]. CrossRef
- I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [SPIRES]. CrossRef
- J.D. Bjorken, Highly relativistic nucleus-nucleus collisions: the central rapidity region, Phys. Rev. D 27 (1983) 140 [SPIRES].
- C.L. Kane and E.J. Mele, Size, shape, and low energy electronic structure of carbon nanotubes, Phys. Rev. Lett. 78 (1997) 1932 [cond-mat/9608146]. CrossRef
- L. Brey and H.A. Fertig, Electronic states of graphene nanoribbons studied with the dirac equation, Phys. Rev. B 73 (2006) 235411 [cond-mat/0603107].
- K. Damle and S. Sachdev, Spin dynamics and transport in gapped one-dimensional heisenberg antiferromagnets at nonzero temperatures, Phys. Rev. B 57 (1998) 8307 [cond-mat/9711014].
- C. Buragohain and S. Sachdev, Intermediate-temperature dynamics of one-dimensional heisenberg antiferromagnets, Phys. Rev. B 59 (1999) 9285 [cond-mat/9811083].
- S. Barrau, P. Demont, A. Peigney, C. Laurent and C. Lacabanne, DC and AC conductivity of carbon nanotubes-polyepoxy composites, Macromolecules 36(14) (2003) 5187. CrossRef
- S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [SPIRES].
- Hydrodynamics of R-charged D1-branes
Journal of High Energy Physics
- Online Date
- January 2011
- Online ISSN
- Additional Links
- Gauge-gravity correspondence
- Holography and condensed matter physics (AdS/CMT)
- Industry Sectors
- 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, Homi-Bhabha Road, Mumbai, 400005, India
- 3. International Centre for Theoretical Sciences, TIFR, Homi-Bhabha Road, Mumbai, 400005, India