Chiral random matrix theory for two-color QCD at high density

Understand

We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density.

• We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective theory at high density, and that the Leutwyler-Smilga-type spectral sum rules of the random matrix theory are identical to those derived from the effective theory.
• The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate.
• We also show that with a different choice of a parameter the random matrix theory yields the effective partition function at low density.