Journal of High Energy Physics
, 2011:14
First online:
Hydrodynamics of Rcharged D1branes
 Justin R. DavidAffiliated withCentre for High Energy Physics, Indian Institute of Science Email author
 , Manavendra MahatoAffiliated withDepartment of Theoretical Physics, TIFR
 , Somyadip ThakurAffiliated withCentre for High Energy Physics, Indian Institute of Science
 , Spenta R. WadiaAffiliated withDepartment of Theoretical Physics, TIFRInternational Centre for Theoretical Sciences, TIFR
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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.
Keywords
Gaugegravity correspondence Dbranes Holography and condensed matter physics (AdS/CMT) 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)
 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