TY - JOUR

T1 - Axial anomaly in the reduced model

T2 - Higher representations

AU - Inagaki, Teruaki

AU - Kikukawa, Yoshio

AU - Suzuki, Hiroshi

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - 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 = Ld). 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 L2 (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.

AB - 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 = Ld). 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 L2 (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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U2 - 10.1088/1126-6708/2003/05/042

DO - 10.1088/1126-6708/2003/05/042

M3 - Article

AN - SCOPUS:23044465788

VL - 7

SP - 973

EP - 992

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 5

ER -