Axial Anomaly and Topological Charge in Lattice Gauge Theory with Overlap Dirac Operator

Abstract

An explicit, detailed evaluation of the classical continuum limit of the axial anomaly and index density of the overlap Dirac operator is carried out in the infinite volume setting and in a certain finite volume setting where the continuum limit involves an infinite volume limit. Our approach is based on a novel power series expansion of the overlap Dirac operator. The correct continuum expression is reproduced when the parameter m0 is in the physical region 0<m0<2. This is established for a broad range of continuum gauge fields. An analogous result for the fermionic topological charge, given by the index of the overlap Dirac operator, is then established for a class of topologically nontrivial fields in the aforementioned finite volume setting. Problematic issues concerning the index in the infinite volume setting are also discussed.