Journal of High Energy Physics

, 2011:14

Hydrodynamics of R-charged D1-branes


    • Centre for High Energy PhysicsIndian Institute of Science
  • Manavendra Mahato
    • Department of Theoretical PhysicsTIFR
  • Somyadip Thakur
    • Centre for High Energy PhysicsIndian Institute of Science
  • Spenta R. Wadia
    • Department of Theoretical PhysicsTIFR
    • International Centre for Theoretical Sciences, TIFR

DOI: 10.1007/JHEP01(2011)014

Cite this article as:
David, J.R., Mahato, M., Thakur, S. et al. J. High Energ. Phys. (2011) 2011: 14. doi:10.1007/JHEP01(2011)014


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.


Gauge-gravity correspondenceD-branesHolography and condensed matter physics (AdS/CMT)

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© SISSA, Trieste, Italy 2011