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 μ. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive “replica trick” fails for μ 6= 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 μ 6= 0 and provide a simple analytical explanation of a long-standing puzzle. Electronic mail address: [email protected]. 1