Global Anomalies in Chiral Lattice Gauge Theories

We study global anomalies in a new approach to chiral gauge theories on the lattice, which is based on the Ginsparg-Wilson relation. In this approach, global anomalies make it impossible to define consistently a. fermionic measure for the functional integral. We show that a global anomaly occurs in an SU (2) theory if the fundamental representation is used for the fermion fields. The generalization to higher rep­ resentations is also discussed: In addition we establish a. close relation between· global anomalies and the spectral flow of the Dirac operator and employ it in a numerical computation to prove the existence of the global SU(2) anomaly in a. different way. This method is inspired by an earlier work of Witten who first discovered this type of anomalies in continuum field theory