Global obstructions to gauge-invariance in chiral gauge theory on the lattice

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e., close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition dR(abc) = 0 is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation. (C) 2000 Elsevier Science B.V. All rights reserved.