Conformal solids and holography

TL;DR

This paper proposes a holographic model of a solid using magnetic monopoles in AdS space, deriving phonon dynamics, and predicting a first-order phase transition from solid to liquid at high temperature.

Contribution

It introduces the concept of a 'solidon' as a holographic dual of a solid state, deriving boundary phonon actions, and analyzing phase transitions with backreaction effects.

Findings

Solidon configuration spontaneously breaks translation symmetry.

Longitudinal and transverse sound speeds are related as expected from effective field theory.

Solidon undergoes a first-order phase transition to a black hole at high temperature.

Abstract

We argue that a $SO(d)$ magnetic monopole in an asymptotically AdS space-time is dual to a $d$-dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration $solidon$. In the presence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary$-$the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.