Colloquium : Hydrodynamics and holography of charge density wave phases

In this Colloquium, we review recent progress in the effective description of strongly-correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is inevitable and pins the Goldstones of broken translations. We describe how pinning can be incorporated in the effective field theory at low energies, without making any assumption on the presence of boost symmetry. We review the essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries. We close with a discussion on the relevance of these models for the phenomenology of dc and ac transport in strongly-correlated strange and bad metals, such as high temperature superconductors.