Spectral sum rules of the Dirac operator and partially quenched chiral condensates

Exploiting Virasoro constraints on the effective finite-volume partition Fu nction, we derive generalized Leutwyler-Smilga spectral sum rules of the Di rac operator to high order. By introducing N-v fermion species of equal mas ses, we next use the Virasoro constraints to compute two (low-mass and larg e-mass) expansions of the partially quenched chiral condensate through the replica method of letting N-v --> 0. The low-mass expansion can only be pus hed to a certain finite order due to de Wit-'t Hooft poles, but the large-m ass expansion can be carried through to arbitrarily high order. Results agr ee exactly with earlier results obtained through both Random Matrix Theory and the supersymmetric method. (C) 2000 Elsevier Science B.V. All rights re served.