  The effect of the complex phase of the fermion determinant is a key question
related to the sign problem in finite-density QCD. Recently it has been shown
that ignoring the complex phase -- the phase quenching -- does not change
physics in a certain region of the phase diagram when a number of colors N_c is
large. In this paper we study the effect of the phase quenching within the
frameworks of effective models and holographic models. We show, in a unified
manner, that the phase quenching gives exact results for any fermionic
observables (e.g., chiral condensate) in the mean-field approximation and for
gauge-invariant gluonic observables (e.g., Polyakov loop) to one-meson-loop
corrections beyond mean field. We also discuss implications for the lattice
simulations and confirm good quantitative agreement between our prediction and
existing lattice QCD results. Therefore the phase quenching provides rather
accurate answer already at N_c=3 with small 1/N_c corrections which can be
taken into account by the phase reweighting.
