A simple model, extracted using holography, of a domain wall between a confining and a de-confining phases and its velocity

In the context of theories with a first order phase transition, we propose a general covariant description of coexisting phases separated by domain walls using an additional order parameter-like degree of freedom. In the case of a holographic dual to a confining and a de-confining phases, the resulting model extends hydrodynamics and has a simple formulation in terms of an action and a corresponding energy-momentum tensor. The proposed description leads to simple analytic profiles of domain walls, including the surface tension density, which agree nicely with holographic numerical solutions. We show that for such systems, the domain wall or bubble velocity can be expressed in a simple way in terms of a perfect fluid hydrodynamic formula, and thus in terms of the equation of state. We test the predictions for various holographic domain walls.