In this thesis I use effective models to investigate the properties of QCD-like
theories at nonzero temperature and baryon chemical potential.
First I construct a PNJL model using a lattice spin model with nearestneighbor
interactions for the gauge sector and four-fermion interactions for
the quarks in (pseudo)real representations of the gauge group. Calculating
the phase diagram in the plane of temperature and quark chemical potential
in QCD with adjoint quarks, it is qualitatively confirmed that the critical
temperature of the chiral phase transition is much higher than the deconfinement
transition temperature. At a chemical potential equal to half of the
diquark mass in the vacuum, a diquark Bose–Einstein condensation (BEC)
phase transition occurs. In the two-color case, a Ginzburg–Landau expansion
is used to study the tetracritical behavior around the intersection point
of the deconfinement and BEC transition lines which are both of second order.
A compact expression for the expectation value of the Polyakov loop in
an arbitrary representation of the gauge group is obtained for any number of
colors, which allows us to study Casimir scaling at both nonzero temperature
and chemical potential.
Subsequently I study the thermodynamics of two-color QCD (QC2D) at
high temperature and/or density using ZQCD, a dimensionally reduced superrenormalizable
effective theory, formulated in terms of a coarse grained
Wilson line. In the absence of quarks, the theory is required to respect the Z2
center symmetry, while the effects of quarks of arbitrary masses and chemical
potentials are introduced via soft Z2 breaking operators. Perturbative
matching of the effective theory parameters to the full theory is carried out
explicitly, and it is argued how the new theory can be used to explore the
phase diagram of two-color QCD.