Finite density QCD via an imaginary chemical potential

We study QCD at nonzero temperature and baryon density in the framework of the analytic continuation from an imaginary chemical potential. We carry out simulations of QCD with four flavors of staggered fermions, and reconstruct the phase diagram in the temperature-imaginary $\mu$ plane. We consider Ansätze for the analytic continuation of the critical line and other observables motivated both by theoretical considerations and mean field calculations in four fermion models and random matrix theory. We determine the critical line, and the analytic continuation of the chiral condensate, up to ${\mu }_B\simeq 500\mathrm{MeV}.$ The results are in qualitative agreement with the predictions of model field theories, and consistent with a first order chiral transition. The correlation between the chiral transition and the deconfinement transition observed at $\mu =0\mathrm{}$ persists at nonzero density.