  Exploiting Virasoro constraints on the effective finite-volume partition
function, we derive generalized Leutwyler-Smilga spectral sum rules of the
Dirac operator to high order. By introducing $N_v$ fermion species of equal
masses, we next use the Virasoro constraints to compute two (low-mass and
large-mass) expansions of the partially quenched chiral condensate through the
replica method of letting $N_v \to 0$. The low-mass expansion can only be
pushed to a certain finite order due to de Wit-'t Hooft poles, but the
large-mass expansion can be carried through to arbitrarily high order. Results
agree exactly with earlier results obtained through both Random Matrix Theory
and the supersymmetric method.
