Black holes dual to helical current phases

We consider the class of $d=4$ conformal field theories at finite temperature and chemical potential that are holographically described within $D=5$ Einstein-Maxwell theory with a Chern-Simons term. The high temperature phase, which is spatially homogeneous and isotropic, is dual to the AdS-Reissner-N\"ordstrom black brane solution. For sufficiently large Chern-Simons coupling, we construct new electrically charged AdS black hole solutions that are dual to the low temperature, spatially modulated phase. In this phase the current, associated with the Abelian global symmetry, spontaneously acquires a helical order. The new black holes are stationary and also have Bianchi VII₀ symmetry.