24 research outputs found
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 ). 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 (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 limit. The large
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.Comment: 21 pages, uses JHEP.cls and amsfonts.sty, the final version to appear
in JHE