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 ei genvalue density of the Dirac matrix on a complex plane. A naive ''rep lica trick'' fails for mu not equal 0; we find that quenched QCD is no t a simple n --> 0 limit of QCD with n quarks. It is the limit of a th eory with 2n quarks: n quarks with original action and n quarks with c onjugate action. The results agree with earlier studies of lattice QCD at mu not equal 0 and provide a simple analytical explanation of a lo ng-standing puzzle.