  We present a unified perspective on Dynamical Mean Field Theory (DMFT),
Density-Matrix Embedding Theory (DMET) and Rotationally Invariant Slave Bosons
(RISB). We show that DMET can be regarded as a simplification of the RISB
method where the quasiparticle weight is set to unity. This relation allows to
easily transpose extensions of a given method to another: for instance, a
temperature-dependent version of RISB can be used to derive a
temperature-dependent free-energy formula for DMET.
