Noncompact chiral U(1) gauge theories on the lattice - art. no. 014503

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact Abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, i n addition, produces a Wess-Zumino functional that is linear in the gauge v ariables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simpl y related, and Berry's curvature now appears as a Schwinger term. The adiab atic phase choice can be further improved to produce a perfect phase choice , with a lattice Wess-Zumino functional that is just as simple as the one i n continuum. When perturbative anomalies cancel, gauge invariance in the fe rmionic sector is fully restored. The lattice effective action describing a n anomalous Abelian gauge theory has an explicit form, close to one analyze d in the past in a perturbative continuum framework.