Chiral Anomalies in the Reduced (or Matrix) Model

TL;DR

This paper demonstrates that chiral anomalies persist in a reduced matrix model with a suitable Dirac operator, revealing their topological nature even without coordinate dependence of gauge fields.

Contribution

It shows that chiral anomalies can be realized in reduced models using Ginsparg-Wilson-type Dirac operators, highlighting their topological origin.

Findings

Chiral anomalies are present in the reduced model with an appropriate Dirac operator.

The anomalies are linked to the topological properties of Ginsparg-Wilson-type operators.

Anomalies persist despite the absence of coordinate dependence in gauge fields.

Abstract

We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological nature of chiral anomalies associated to Ginsparg-Wilson-type lattice Dirac operators.