Abstract
We use holographic correspondence to study transport of the conformal plasma in ${\mathbb{R}}^{2,1}$ in a phase with a spontaneously broken global ${\mathbb{Z}}_{2}$ symmetry. The dual black branes in a Poincare patch of asymptotically ${\mathrm{AdS}}_{4}$ 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 ${c}_{s}^{2}=\frac{1}{2}$. We compute the low-lying spectrum of the nonhydrodynamic modes. We identify a quasinormal mode associated with the fluctuations of the ${\mathbb{Z}}_{2}$ 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.
Highlights
Following the general suggestion of [1], we proposed in [2]1 a holographic model for a conformal order2: a thermal phase of a conformal gauge theory in R2;1 with a nonzero expectation value of an irrelevant, dimension Δ 1⁄4 4 operator O, spontaneously breaking the global Z2 symmetry
We find that the thermodynamics of all the symmetry broken phases resemble that of the symmetric phase in the limit b → −∞, ð1
We explicitly demonstrate that the symmetry breaking phases at finite b are robust against the deformation (7), for small enough g > 0
Summary
Following the general suggestion of [1], we proposed in [2]1 a holographic model for a conformal order: a thermal phase of a conformal gauge theory in R2;1 with a nonzero expectation value of an irrelevant, dimension Δ 1⁄4 4 operator O, spontaneously breaking the global Z2 symmetry. We study the coupled metric-scalar fluctuations in the symmetry broken phases of (2) and compute the spectrum of the quasinormal modes (QNMs) of the black branes dual to the conformal order on the lowest branch.. Besides the sound wave—a hydrodynamic QNM in the scalar channel [5]—there are two branches of the nonhydrodynamic modes coming from the mixing of the helicity zero metric fluctuations in the equilibrium black brane geometry and the gravitational bulk scalar field, whose boundary values determine the order parameter for the Z2 symmetry breaking. Im1⁄2wuðq 1⁄4 0Þ > 0; as b ∈ ð−∞; bcrit;0Þ; ð13Þ approaching zero in the limit b → bcrit;0 The presence of this mode in the spectrum implies that the translational invariant horizon of the black brane dual to a conformal order is perturbatively unstable to clumping. A challenge remains to find an example of a stable holographic thermal conformal order—a phase of the black branes which is both the dominant one in the canonical ensemble, and is perturbatively stable with respect to the linearized fluctuations
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