Chiral anomalies in the reduced model

Abstract

On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N\to \infty$ limit when d>2.

20 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHEP

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• Admissibility Condition and Nontrivial Indices on a Noncommutative Torus
• Anomalous gauge theories revisited
• Lattice Superstring and Noncommutative Geometry
• Axial anomaly in the reduced model: Higher representations
• Wess-Zumino-Witten term on the lattice
• Four-dimensional lattice chiral gauge theories with anomalous fermion content
• Axial anomaly in the reduced model: Higher representations