Chiral anomalies in the reduced model

On the basis of an observation due to Kiskis, Narayanan and Neuberger, weshow that there is a remnant of chiral anomalies in the reduced model when aDirac operator which obeys the Ginsparg-Wilson relation is employed for thefermion sector. We consider fermions belonging to the fundamentalrepresentation of the gauge group U(N) or SU(N). For vector-like theories, wedetermine a general form of the axial anomaly or the topological charge withina framework of a U(1) embedding. For chiral gauge theories with the gauge groupU(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermionintegration measure. The pure gauge action of gauge-field configurations whichcause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$limit when d>2.Comment: 20 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE