Instability of Baryonic Black Branes

Baryonic black branes describe the quantum critical phase of the conformal conifold gauge theory at strong coupling. This phase extends to zero temperature at a finite baryonic chemical potential, represented by extremal black branes with $AdS_2\times R^3\times T^{1,1}$ throat in asymptotic $AdS_5\times T^{1,1}$ geometry. We demonstrate here that this phase is dynamically unstable below some critical value of $T_c/\mu$: the instability is represented by a diffusive mode in the hydrodynamic sound channel with a negative diffusion coefficient. We also identify a new (exotic) ordered phase of the conifold gauge theory: this phase originates at the same critical value of $T_c/\mu$, but extends to arbitrary high temperatures, and is characterized by an expectation value of a dimension-2 operator, ${\cal O}_2\propto T^2$, in the limit $\frac \mu T\to 0$.