The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds Original Research Article

We study the spectral flow of the hermitian Wilson-Dirac operator H(m) as a function of m in smooth SU(2) instanton backgrounds on the lattice. For a single instanton background with Dirichlet boundary conditions on H(m), we find a level crossing in the spectral flow of H(m), with the zero-mode associated with the single instanton background. With anti-periodic boundary conditions on H(m), we find that the instanton background in the singular gauge has the correct spectral flow but the one in regular gauge does not. We also investigate the spectral flows of two instanton and instanton-anti-instanton backgrounds.