Instability of baryonic black branes

A bstract 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 × R 3 × T 1,1 throat in asymptotic AdS 5 × T 1,1 geometry. We demonstrate here that this phase is dynamically unstable below some critical value of T c / μ : 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 / μ , but extends to arbitrary high temperatures, and is characterized by an expectation value of a dimension-2 operator, $$ {\mathcal{O}}_2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ∝ T 2 , in the limit $$ \frac{\mu }{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mi>μ</mml:mi> <mml:mi>T</mml:mi> </mml:mfrac> </mml:math> → 0.