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

P.H. Damgaard, K. Splittorff
2000 Nuclear Physics B  
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
more » ... der 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.
doi:10.1016/s0550-3213(00)00022-5 fatcat:pn5jfre7t5csbfhspc34ebvxa4