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 invariance or violating any other fundamental principle. The Ginsparg-Wilson relation plays a key role in this construction, which is non-perturbative and includes all topological sectors of the theory in finite volume. In particular, the cancellation of the gauge anomaly and the absence of global topological obstructions can be established on the basis of this relation and the lattice symmetries alone.