Chiral anomalies in the reduced model

TL;DR

This paper investigates the persistence of chiral anomalies in reduced models using Ginsparg-Wilson Dirac operators, revealing anomalies and obstructions in fermion measures and gauge configurations in large N limits.

Contribution

It demonstrates the existence of chiral anomaly remnants in reduced models with Ginsparg-Wilson fermions and characterizes their impact on gauge theories at large N.

Findings

Chiral anomalies persist in reduced models with Ginsparg-Wilson fermions.

Gauge anomalies manifest as obstructions to smooth fermion measures.

Certain gauge configurations cause divergence in the large N limit.

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.