Axial anomaly in the reduced model: Higher representations

Abstract

The axial anomaly arising from the fermion sector of $\text{U}(N)$ or $\text{SU}(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\text{U}(1)$ embedding'' with $N=L^d$). 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 $L^2$ (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. Nevertheless, when the gauge group is $\text{SU}(N)$, it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.

Comments: 21 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHEP