The SU(N) Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to Nf flavors of massless quarks, the Euclidean Dirac equation in an instanton background has n+ positive and n− negative chirality zero modes. We show that the index (n+−n−) is equal to a suitably defined instanton charge. Further, we show that the path integral measure is not invariant under a chiral rotation, and relate the non-invariance of the measure to the index of the Dirac operator. Axial symmetry is broken anomalously, with the residual symmetry being a finite group. For Nf fundamental fermions, this residual symmetry is Z2Nf, whereas for adjoint quarks it is Z4Nf.
Finally, we remark on the importance of the chiral anomaly for the QCD SU(3) gauge matrix model.
