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QCD-like theories at nonzero temperature and density. (English) Zbl 1288.81152
Summary: We investigate the properties of hot and/or dense matter in QCD-like theories with quarks in a (pseudo)real representation of the gauge group using the Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice spin model with nearest-neighbor interactions. We first keep our discussion as general as possible, and only later focus on theories with adjoint quarks of two or three colors. Calculating the phase diagram in the plane of temperature and quark chemical potential, 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. We obtain a compact expression for the expectation value of the Polyakov loop in an arbitrary representation of the gauge group (for any number of colors), which allows us to study Casimir scaling at both nonzero temperature and chemical potential.

##### MSC:
 81V05 Strong interaction, including quantum chromodynamics 81R40 Symmetry breaking in quantum theory 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 81T28 Thermal quantum field theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B30 Statistical thermodynamics 82B27 Critical phenomena in equilibrium statistical mechanics
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