Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

Understand

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu.

• In this symmetry class the determinant of the Dirac operator is real but not necessarily positive.
• Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled.
• We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours.