The Sound of M-Theory

TL;DR

The paper investigates sound propagation in the finite-temperature field theories on M2- and M5-branes using the AdS/CFT correspondence. It computes Lorentzian stress-energy tensor two-point functions from eleven-dimensional supergravity and finds hydrodynamic sound poles with speeds u_s = 1/√d (d = 2 for M2, d = 5 for M5) and damping governed by η/(ε+P), in agreement with fluid dynamics. The results validate Ward identities and a Lorentzian gravity-to-field-theory mapping, providing strong evidence for the holographic description of M-brane hydrodynamics and supporting potential extensions to non-conformal theories.

Abstract

We consider sound propagation on M5- and M2-branes in the hydrodynamic limit. In particular, we look at the low energy description of a stack of N M-branes at finite temperature. At low energy, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. From this gravitational description, we calculate Lorentzian signature two-point functions of the stress-energy tensor on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit. The poles in these Green's functions show evidence for sound propagation in the field theory living on the M-branes.