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We study generic properties of strongly interacting matter at finite densityas relevant to heavy-ion collisions at moderate beam energies or the physics ofneutron stars and their mergers. Because of the fermion-sign problem in latticeQCD, here we simulate QCD-like theories without this problem at finite density.These theories (two-color QCD, G2-QCD, or adjoint QCD) typically containbosonic baryons, for example diquarks, or other more exotic states of matter.It is therefore important to understand the effects of such bosonic matter anddisentangle them from fermionic baryons where they exist to draw conclusionsfor QCD. Simulations of these theories, for instance G2-QCD, reveal aninteresting and rich phase diagram at zero temperature. Many open questionsarise, partly due to the lack of high precision or large volume/continuum data.This is the reason why we study two-dimensional QCD-like theories. In thiscontribution we shall discuss differences between QCD-like theories at baryonchemical and isospin chemical potential. Furthermore we present simulationresults on the phase diagram and spectroscopy at finite density for G2- andtwo-color-QCD and compare it to free lattice fermions.

What we can learn from two-dimensional QCD-like theories at finite density