Effective theory for quenched lattice QCD and the Aoki phase

TL;DR

This paper develops an effective theory for quenched lattice QCD with Wilson fermions, analyzing its phase structure and comparing it to unquenched QCD, with implications for numerical simulations using various fermion formulations.

Contribution

It constructs the chiral effective Lagrangian for quenched QCD, including lattice spacing effects, and studies its phase structure, especially the Aoki phase, in relation to unquenched QCD.

Findings

The phase structure in quenched QCD is qualitatively similar to unquenched QCD.

The presence of an Aoki phase or a first order transition depends on a parameter's sign.

Implications for numerical studies with overlap and domain-wall fermions are discussed.

Abstract

We discuss the symmetries of quenched QCD with Wilson fermions, starting from its lagrangian formulation, taking into account the constraints needed for convergence of the ghost-quark functional integral. We construct the corresponding chiral effective lagrangian, including terms linear and quadratic in the lattice spacing. This allows us to study the phase structure of the quenched theory, and compare it to that in the unquenched theory. In particular we study whether there may be an Aoki phase (with parity and flavor spontaneously broken) or a first order transition line (with no symmetry breaking but meson masses proportional to the lattice spacing), which are the two possibilities in the unquenched theory. The presence of such phase structure, and the concomitant long-range correlations, has important implications for numerical studies using both quenched and dynamical overlap and domain-wall fermions. We argue that the phase structure is qualitatively the same as in the unquenched theory, with the choice between the two possibilities depending on the sign of a parameter in the low-energy effective theory.