Abelian chiral gauge theories on the lattice with exact gauge invariance

It is shown that U(1) chiral gauge theories with anomaly free multiplets of Weyl fermions can be put on the lattice without breaking the gauge invaria nce or violating any other fundamental principle. The Ginsparg-Wilson relat ion plays a key role in this construction, which is nonperturbative and inc ludes all topological sectors of the theory in finite volume. In particular , the cancellation of the gauge anomaly and the absence of global topologic al obstructions can be established on the basis of this relation and the la ttice symmetries alone. (C) 1999 Elsevier Science B.V. All rights reserved.