After reviewing the gravitational dual of superfluids in the context of AdS/CFT, I will describe an analytical method to derive the low-energy spectrum of the boundary theory. The result confirms that, at zero temperature, the effective theory consists of a longitudinal phonon with the correct speed of sound. I will next move on to consider the EFT of solids and use it to motivate the construction of a holographic dual. Here too we are able to derive the correct low-energy effective theory of the phonons in a conformally invariant solid. Lastly we obtain some numerical solutions including backreaction and calculate the free energy, finding evidence that the system “melts'' into a black hole as the temperature is raised, which we interpret as a solid-to-liquid phase transition on the field theory side.

Institut d’Astrophysique de Paris