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

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 Nv 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 Nv→0. The low-mass expansion can only be pushed to a certain finite order due to de Wit–ʹt 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.