Colloquium: Hydrodynamics and holography of charge density wave phases

The Colloquium reviews 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. The Colloquium describes how pinning can be incorporated into the effective field theory at low energies without making any assumptions on the presence of boost symmetry. The essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries is reviewed. The Colloquium closes with a discussion on the relevance of these models to the phenomenology of dc and ac transport in strongly correlated strange and bad metals, such as high-temperature superconductors.