Two roads to hydrodynamic effective actions: a comparison

We make a detailed comparison between two attempts in recent years to construct hydrodynamic effective actions: we compare our work [1-7] with that of Crossley-Glorioso-Liu [8] and Glorioso-Liu [9]. The general philosophy espoused by the two approaches has a degree of overlap, despite various differences. We will try to outline the similarities to eke out the general lessons that have been uncovered, hoping that it will ease the access to the subject for interested readers.