"A Holographic Dual of Spatially Modulated Phase at Finite Densities"

We propose a holographic dual of spatially modulated phase that may be realized at finite densities. In the gauge/gravity duality, thermal equilibrium is often realized by the presence of a black hole, and a global symmetry in the YM theory is promoted to a gauge symmetry in the gravity dual. Therefore, a black hole charged under the bulk gauge symmetry represents the finite-density system of the YM theory under the corresponding global symmetry. Furthermore, if we derive the gravity theory starting from superstring theory, we often have a Chern-Simons term which provides an interacting term for the bulk gauge field. With these general properties of gauge/gravity duality in mind, we analyzed a 5-dimensional charged black holes under the presence of Chern-Simons terms. We found that if the Chern-Simons coupling and the charge density are large enough, the black hole becomes unstable against spatially inhomogeneous condensation of the bulk gauge field, suggesting that the presence of a spatially modulated phase in the YM side where translational and rotational symmetries are spontaneously broken.