Axial anomaly in the reduced model: Higher representations

Teruaki Inagaki, Yoshio Kikukawa, Hiroshi Suzuki

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Abstract

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.

Original languageEnglish
Pages (from-to)973-992
Number of pages20
JournalJournal of High Energy Physics
Volume7
Issue number5
Publication statusPublished - May 1 2003
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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