Partially Quenched Chiral Perturbation Theory and the Replica Method

TL;DR

This paper introduces a new, simple framework for partially quenched chiral perturbation theory using the replica method, demonstrating its equivalence to supersymmetric approaches and enabling smooth transitions between them.

Contribution

It presents a novel replica-based framework for partially quenched chiral perturbation theory, simplifying calculations and establishing equivalence with supersymmetric methods.

Findings

Replica method rules are exceedingly simple.

Explicit one-loop order calculation of the chiral condensate.

Demonstrates equivalence between replica and supersymmetric methods.

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.