String inspired solution to the sign problem and overlapping problem

Because of the sign problem, it is difficult to study finite-density QCD. In order to circumvent the sign problem, we prove that the phase-quenched approximation is exact to O(Nf/Nc) for any physical observables in a certain region of the phase diagram. We also find a quantitative evidence for the validity of the phase quenching from existing lattice QCD results at Nc = 3. Our results show that the phase-quenched approximation is good already at Nc = 3, and the 1/Nc correction can be incorporated by the phase reweighting method without suffering from a severe overlap problem. The same equivalence holds in effective models and holographic models. It gives us a theoretical understanding of the empirical facts (exactness of the phase quenching in the mean-field approximation) found in model calculations.