Axial anomaly in the reduced model: Higher representations

TL;DR

This paper investigates the topological charge in the large N limit of a reduced model with fermions in higher representations, using the overlap Dirac operator and a specific gauge field configuration restriction called U(1) embedding.

Contribution

It introduces a method to define topological charge in the large N limit for higher representation fermions using the overlap Dirac operator under U(1) embedding.

Findings

Large N limit of topological charge obtained

Application of overlap Dirac operator in reduced models

Extension to fermions in general gauge-group representations

Abstract

The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed $\U(1)$ embedding.