Hydrodynamics of R-charged D1-branes

TL;DR

This paper investigates the hydrodynamic behavior of strongly coupled D1-brane gauge theory at finite temperature and R-charge density using gauge/gravity duality, revealing universal ratios and critical phenomena.

Contribution

It provides exact calculations of transport coefficients for R-charged D1-branes and uncovers their relation to M2-brane transport properties, including universal ratios and critical behavior.

Findings

Bulk viscosity to entropy density ratio is 1/4π, independent of chemical potential.

Thermal conductivity and bulk viscosity follow a Wiedemann-Franz-like law.

Charge diffusion mode becomes unstable at thermodynamic stability boundary.

Abstract

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.