Chiral Anomaly for a New Class of Lattice Dirac Operators

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 $a\to 0$.

Comments: 23 pages. Corrected typos and misprints. Made several sentences more precise, and references up-dated. (To appear in Nucl. Phys. B)