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 $a\to 0$.

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

References in corpus (3)

• Bounds on the Wilson Dirac Operator
• Relation $Tr{\gamma }_5=0$ and the index theorem in lattice gauge theory
• One-loop analyses of lattice QCD with the overlap Dirac operator

Cited by in corpus (13)

• Nicolai mapping vs. exact chiral symmetry on the lattice
• Lattice chiral symmetry, Yukawa couplings and the Majorana condition
• Two-photon decay of the neutral pion in lattice QCD
• Lattice Chiral Symmetry and the Wess-Zumino Model
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Ginsparg-Wilson operators and a no-go theorem
• CP breaking in lattice chiral gauge theories
• Locality Properties of a New Class of Lattice Dirac Operators
• More about the axial anomaly on the lattice
• Domain wall fermion and CP symmetry breaking
• A Perturbative Study of a General Class of Lattice Dirac Operators
• General chiral gauge theories on the lattice
• Chiral fermion operators on the lattice