Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality

Abstract

We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times. Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions. At the chiral point, the characteristic determinant in the microscopic limit is universal. Remarkably, the physical chiral condensate at finite chemical potential may be extracted from current and quenched lattice Dirac spectra using the universal edge scaling laws, without having to solve the QCD sign problem.