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

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaumé 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 dRabc=0 is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation.