  We analytically study two-color QCD with an even number of flavors at high
baryon density. This theory is free from the fermion sign problem. Chiral
symmetry is broken spontaneously by the diquark condensate. Based on the
symmetry breaking pattern we construct the low-energy effective Lagrangian for
the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon
density in which the quark mass dependence of the partition function can be
determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for
the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our
results can in principle be tested in lattice QCD simulations.
