Can nonlocal Dirac operators be topologically proper ?

Abstract

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge.

12 pages, LaTeX, 1 EPS figure, topos corrected and minor changes

References in corpus (3)

• Bounds on the Wilson Dirac Operator
• Algebraic Generalization of the Ginsparg-Wilson Relation
• Some remarks on the Ginsparg-Wilson fermion

Cited by in corpus (6)

• Lattice chiral symmetry, Yukawa couplings and the Majorana condition
• Lattice Chiral Symmetry and the Wess-Zumino Model
• Ginsparg-Wilson operators and a no-go theorem
• Domain wall fermion and CP symmetry breaking
• A Perturbative Study of a General Class of Lattice Dirac Operators
• Free fermionic propagators on a lattice