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تسجيل مستخدم جديدAxial anomaly in the reduced model: Higher representations
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تأليف
Teruaki Inagaki
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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 $N=L^d$). 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 $SU(N)$, 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.
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