A note on causal hydrodynamics for M-theory branes

TL;DR

The paper investigates causal (second-order) hydrodynamics for gauge theory plasmas via AdS/CFT by applying a Kubo-like tensor-mode formula to extract the relaxation time tau_pi and the coefficient kappa for M2- and M5-brane backgrounds. Tensor-mode analyses in SAdS7 and SAdS4 yield tau_pi values that agree with sound-mode results but not with shear-mode estimates, and provide kappa for SAdS7, validating the conformal-formula approach for these theories. The results contribute explicit transport-coefficient values and highlight the non-universality of kappa across different theories, while discussing limitations when extending to non-conformal brane systems (D4/D1). Overall, the work reinforces the utility and caveats of tensor-mode Kubo formulas in holographic causal hydrodynamics and informs potential connections to QCD-inspired physics.

Abstract

We obtain new transport coefficients of causal hydrodynamics for the M2 and the M5-brane using a Kubo-like formula proposed by Baier, Romatschke, Son, Starinets, and Stephanov (arXiv:0712.2451 [hep-th]). The relaxation times agree with the ones obtained from the "sound mode" in our paper (arXiv:0712.2916 [hep-th]).