Fate of the conformal order

We use holographic correspondence to study transport of the conformal plasma in ${\mathbb R}^{2,1}$ in a phase with a spontaneously broken global $Z_2$ symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have "hair" -- a condensate of the order parameter for the broken symmetry. This hair affects both the hydrodynamic and the nonhydrodynamic quasinormal modes of the black branes. Nonetheless, the shear viscosity of the conformal order is universal, the bulk viscosity vanishes and the speed of the sound waves is $c_s^2=\frac 12$. We compute the low-lying spectrum of the non-hydrodynamic modes. We identify a quasinormal mode associated with the fluctuations of the $Z_2$ order parameter with the positive imaginary part. The presence of this mode in the spectrum renders the holographic conformal order perturbatively unstable. Correspondingly, the dual black branes violate the correlated stability conjecture.