The authors study the symmetric exclusion process in the fluctuating hydrodynamic scaling where the occupation number density is described by a Langevin equation. In this set-up they analyze the dynamical large deviations for the activity which is, in this context, by the numbers of hopping that the system perform. It is shown show that a dynamical second order phase transition takes place between a homogeneous state and a kink-like profile for the activity.