Noncompact chiral U(1) gauge theories on the lattice

TL;DR

This paper introduces a new adiabatic phase choice for the overlap in noncompact abelian chiral gauge theories on the lattice, ensuring gauge invariance and simplifying the Wess-Zumino functional.

Contribution

It proposes a novel adiabatic phase choice that maintains symmetries and simplifies anomaly analysis in lattice chiral gauge theories.

Findings

No gauge violations on the trivial orbit

Consistent and covariant anomalies are simply related

Berry's curvature appears as a Schwinger term

Abstract

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, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic 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 in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.