Chiral Anomaly for a New Class of Lattice Dirac Operators

TL;DR

This paper investigates a new class of lattice Dirac operators satisfying a specific algebraic relation, analyzing their chiral anomaly and index theorem, and confirming the anomaly's independence from certain parameters and its correct continuum limit.

Contribution

It introduces and analyzes a novel class of lattice Dirac operators that satisfy the index theorem, extending the understanding of chiral anomalies on the lattice.

Findings

Anomaly coefficient is independent of parameters r and m0.

Correct chiral anomaly is obtained in the continuum limit a→0.

The new operators satisfy the index theorem and reproduce continuum physics.

Abstract

A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and $k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the chiral anomaly and index theorem for all these Dirac operators in an explicit elementary manner. We show that the coefficient of anomaly is independent of a small variation in the parameters $r$ and $m_{0}$, which characterize these Dirac operators, and the correct chiral anomaly is obtained in the (naive) continuum limit $a\to 0$.