QCD-like Theories at Finite Baryon and Isospin Density

We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, $\mu_I$, and for baryon number, $\mu_B$. We determine the phase diagrams for 2 and 4 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 2 colour 2 flavor theory, while we do not expect it the 4 flavor case or in other realizations of QCD with a positive measure.