  We introduce a two-flavor quark-meson-diquark model for two-color QCD and its
extensions to include gauge-field dynamics as described by the Polakov loop.
Grand potential and phase structure are being studied both in mean-field
approximation and with the functional renormalization group. The model provides
an explicit example for the importance of baryonic degrees of freedom: When
they are omitted, the phase diagram closely resembles that of the corresponding
(Polyakov)-quark-meson models for QCD, in particular including their critical
endpoint. In order to reproduce the well established main features based on the
symmetries and breaking patterns of two-color QCD, however, they must be
included and there is no critical endpoint. The competing dynamics of
collective mesonic and baryonic fluctuations is well described by the
functional renormalization group equation in lowest order derivative expansion
for the effective potential which we solve numerically on a two-dimensional
grid in field space.
