Effective holographic theory of charge density waves

We use Gauge/Gravity duality to define an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. Whilst we mostly focus on the leading two-derivative action, we show that including subleading quartic derivative terms leads to dynamical instabilities of the translation invariant ground state. We compute analytically the bulk and shear moduli, shear viscosity and electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating.