Random matrix model of QCD at finite density and the nature of the quenched limit

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential mu. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ''replica trick'' fails for mu not equal 0; we find that quenched QCD is not a simple n --> 0 limit of QCD with n quarks. It is the limit of a theory with 2n quarks: n quarks with original action and n quarks with conjugate action. The results agree with earlier studies of lattice QCD at mu not equal 0 and provide a simple analytical explanation of a long-standing puzzle.