Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane

TL;DR

This paper calculates second order transport coefficients for various Dp-branes using fluid/gravity duality, revealing dimension-dependent relations and the need for generalized formulas beyond 4D.

Contribution

It provides the first comprehensive derivation of second order transport coefficients for Dp-branes with p from 1 to 6, extending fluid/gravity correspondence to nonconformal fluids in multiple dimensions.

Findings

Haack-Yarom relation holds for p > 2 Dp-branes.

Romatschke and Kleinert-Probst relations require generalization outside 4D.

D3-brane corresponds to conformal 4D fluid; others to nonconformal fluids.

Abstract

We derive all the dynamical second order transport coefficients for Dp-brane with $p$ from 1 to 6 within the framework of fluid/gravity correspondence in this paper. The D5 and D6-brane do not have dual relativistic fluids; D3-brane corresponds to 4-dimensional conformal relativistic fluid; D1, D2 and D4-brane separately correspond to nonconformal relativistic fluids of dimensions 2, 3 and 5. The Haack-Yarom relation only exists for Dp-branes with $p$ larger than 2 and is also satisfied by them. We also find that the Romatschke and Kleinert-Probst relations need to be generalized in order to be valid for relativistic fluids of dimensions other than 4.