Lattice Index Theorem and Fractional Topological Charge

Abstract

American Physical Society, One Research Road, Ridge, NY 11961, USA(Dated: October 12, 2010)We study topological properties of classical spherical center vortices with the low-lying eigenmodesof the Dirac operator in the fundamental and adjoint representations using both the overlap andasqtad staggered fermion formulations. In particular we address the puzzle raised in a previouswork of our group [Phys. Rev. D 77, 14515 (2008)], where we found a violation of the lattice indextheorem with the overlap Dirac operator in the fundamental representation even for “admissible”gauge fields. Here we confirm the discrepancy between the topological charge and the index of theDirac operator also for asqtad staggered fermions and the adjoint representation. Numerically, thediscrepancy equals the sum of the winding numbers of the spheres when they are regarded as maps