Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes

Abstract

We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, near-extremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the ${\tau }_{\pi },{\tau }_{\pi }^{\ast },{\tau }_{\Pi },{\lambda }_{1,2,3}$ and ${\xi }_{1,2,3}$ for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation $4{\lambda }_1+{\lambda }_2=2\eta {\tau }_{\pi }$.

Comments: 41 pages and 4 tables