Violations of the Lattice Index Theorem for Spherical Center Vortices

We address the puzzle raised in a previous work of our group [Phys. Rev. D 77, 14515 (2008)], where we found a violation of the lattice index theorem with the overlap Dirac operator in the fundamental representation even for "admissible" gauge fields of a classical, spherical center vortex. Here we confirm the discrepancy between the topological charge and the index of the Dirac operator also for asqtad staggered fermions and adjoint representations. Numerically, the discrepancy equals the sum of the winding numbers of the spheres when they are regarded as maps S-3 -> SU(2).