Chiral Random Two-Matrix Theory and QCD with imaginary chemical potential

摘要

We summarise recent results for the chiral Random Two-Matrix Theoryconstructed to describe QCD in the epsilon-regime with imaginary chemicalpotential. The virtue of this theory is that unquenched Lattice simulations canbe used to determine both low energy constants Sigma and F in the leading orderchiral Lagrangian, due to their respective coupling to quark mass and chemicalpotential. We briefly recall the analytic formulas for all density andindividual eigenvalue correlations and then illustrate them in detail in thesimplest, quenched case with imaginary isospin chemical potential. Somepeculiarities are pointed out for this example: i) the factorisation of densityand individual eigenvalue correlation functions for large chemical potentialand ii) the factorisation of the non-Gaussian weight function of bi-orthogonalpolynomials into Gaussian weights with ordinary orthogonal polynomials.