QCD-like theories at finite baryon and isospin density

We use two-color QCD as a model to study the effects of the simultaneous presence of chemical potentials for isospin charge ${\mu }_I$ and for baryon number ${\mu }_B.$ We determine the phase diagrams for two and four flavor theories using the method of effective chiral Lagrangians at low densities and weak-coupling perturbation theory at high densities. We determine the values of various condensates and densities as well as the spectrum of excitations as functions of ${\mu }_I$ and ${\mu }_B.$ A similar analysis of QCD with quarks in the adjoint representation is also presented. Our results can be of relevance for lattice simulations of these theories. We predict a phase of inhomogeneous condensation (Fulde-Ferrel-Larkin-Ovchinnikov phase) in the two color, two flavor theory, while we do not expect it in the four flavor case or in other realizations of QCD with a positive measure.