The Hydrodynamics of M-Theory

TL;DR

This study extends holographic hydrodynamics to M-theory by computing Minkowski-space two-point functions for R-currents and stress-energy tensors in nonextremal M2- and M5-brane backgrounds. Using the Son-Starinets prescription, it extracts diffusion constants and viscosities, revealing N-dependent scaling behaviors: D_R is N-independent, while η and S scale with N in ways tied to the brane type (N^3 for M5, N^{3/2} for M2). The results satisfy hydrodynamic relations such as D = η/(ε+P) and provide new insights into the transport properties of M-brane theories, along with intriguing N-puzzles that may illuminate M-theory degrees of freedom. Overall, the work demonstrates a consistent hydrodynamic regime for M-branes and motivates further understanding of their microscopic underpinnings.

Abstract

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.