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We discuss the symmetries of quenched QCD with Wilson fermions, starting fromits lagrangian formulation, taking into account the constraints needed forconvergence of the ghost-quark functional integral. We construct thecorresponding chiral effective lagrangian, including terms linear and quadraticin the lattice spacing. This allows us to study the phase structure of thequenched theory, and compare it to that in the unquenched theory. In particularwe study whether there may be an Aoki phase (with parity and flavorspontaneously broken) or a first order transition line (with no symmetrybreaking but meson masses proportional to the lattice spacing), which are thetwo possibilities in the unquenched theory. The presence of such phasestructure, and the concomitant long-range correlations, has importantimplications for numerical studies using both quenched and dynamical overlapand domain-wall fermions. We argue that the phase structure is qualitativelythe same as in the unquenched theory, with the choice between the twopossibilities depending on the sign of a parameter in the low-energy effectivetheory.Comment: 31 pages, a few minor correction

Effective theory for quenched lattice QCD and the Aoki phase