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We discuss a random matrix theory that was originally constructed to describetwo-color QCD at low density in the phase with a nonzero chiral condensate.With a particular choice of a parameter, the same random matrix theory alsodescribes the high-density phase of two-color QCD. In this phase a BCSsuperfluid of diquark pairs is formed, and the pattern of chiral symmetrybreaking is very different from that at low density. Analytical results for thespectral density obtained from this random matrix theory allow for theextraction of the BCS gap from lattice data.

Exact results for two-color QCD at low and high density