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.