Axial anomaly in the reduced model: Higher representations

The axial anomaly arising from the fermion sector of U(N) or SU(N) reduced model is studied under a certain restriction of gauge field configurations (the “U(1) embedding” with N = L). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of L (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large N limit. The large N limit exhibits expected algebraic properties as the axial anomaly.