Partially Quenched Chiral Perturbation Theory and the Replica Method

Abstract

We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rules by computing the partially quenched chiral condensate to one-loop order. By considering arbitrary chiral $k$-point functions we show explicitly to one-loop order the equivalence between this method and the one based on supersymmetry. It is possible to go smoothly from the conventional replica method to a supersymmetric variant by choosing the number of valence quarks to be negative.