Zusammenfassung
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 \$1/4\pi\$. 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.
Nutzer