Global anomalies in chiral gauge theories on the lattice

We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Lüscher's approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU(2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show that this obstruction is the lattice analogue of the SU(2) anomaly first discovered by Witten