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

Abstract

We derive all the dynamical second order transport coefficients for Dpbrane 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.

Second order transport coefficients of nonconformal fluids from compactified Dp-branes

“…This section shows how to reduce the 10 dimensional background of Dp-brane to a p − q + 2 dimensional spacetime. Since this work is subsequent to [26], the conventions are the same JHEP05(2021)262 as that reference. We will then be brief in offering the details of the definitions which are the same as before and will also stress the differences.…”

“…is the volume of the compact directions on the Dp-brane world-volume. 2κ 2 p−q+2 is the surface gravity of the p − q + 2 dimensional reduced gravity theory and it relates with that of Dp-brane [26] by…”

“…Based on these previous works, [23][24][25][26] calculate the first and second order transport coefficients for D-branes via the fluid/gravity correspondence and have got some new results. Of those references, [23,24] study the D4-brane with 1 world-volume direction compact and [26] calculates all the dynamical second order transport coefficients for Dpbrane.…”

“…Based on these previous works, [23][24][25][26] calculate the first and second order transport coefficients for D-branes via the fluid/gravity correspondence and have got some new results. Of those references, [23,24] study the D4-brane with 1 world-volume direction compact and [26] calculates all the dynamical second order transport coefficients for Dpbrane. This paper can be seen as a follow-up work of [26] and we are aiming to calculate all the dynamical second order transport coefficients for Dp-brane with q of its world-volume direction(s) compactified, where 1 ≤ q ≤ p − 1.…”

“…Of those references, [23,24] study the D4-brane with 1 world-volume direction compact and [26] calculates all the dynamical second order transport coefficients for Dpbrane. This paper can be seen as a follow-up work of [26] and we are aiming to calculate all the dynamical second order transport coefficients for Dp-brane with q of its world-volume direction(s) compactified, where 1 ≤ q ≤ p − 1. This can be seen as our first motivation.…”