Axial Anomaly in SU(N) Yang-Mills Matrix Models.

The SU(N) Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to N_{f} flavors of massless quarks, the Euclidean Dirac equation in an instanton background has n_{+} positive and n_{-} negative chirality zero modes. The vacua of the gauge theory are N-dimensional representations of SU(2), and the (anti-) self-dual instantons tunnel between two commuting representations, the initial one composed of r_{0}^{(1)} irreps and the final one with r_{0}^{(2)} irreps.