A lattice version of the Atiyah-Singer index theorem

Abstract

We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a $K$-theoretic formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds. We apply the main theorem to an index problem of Wilson-Dirac operators in lattice gauge theory.

arXiv comment27 pages, final version

References in corpus (5)

• The index theorem in QCD with a finite cut-off
• Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly
• Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator
• On the continuum limit of fermionic topological charge in lattice gauge theory
• Atiyah-Patodi-Singer index on a lattice

Cited by in corpus (1)

• $K$-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators