Sign problem and phase quenching in finite-density QCD: Models, holography, and lattice

Abstract

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 the expectation values of a class of observables in a certain region of the phase diagram when a number of colors 𝑁𝑐 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 a class of 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 a rather accurate answer already at 𝑁𝑐 =3 with small 1/𝑁𝑐 corrections which can be taken into account by the phase reweighting.