Novel Lattice Formulation of 2D Chiral Gauge Theory via Bosonization

TL;DR

This paper introduces a new lattice formulation for 2D chiral gauge theories using the excision method, which respects admissibility and allows for defining magnetic objects as lattice defects, advancing the understanding of anomaly reproduction.

Contribution

It proposes a novel lattice approach based on the excision method that maintains admissibility and enables the definition of magnetic objects as lattice defects.

Findings

The excision method respects the admissibility condition.

Magnetic objects can be represented as lattice defects called 'holes'.

The approach reproduces the gauge anomaly structure of continuum theories.

Abstract

Recently, lattice formulations of 2D Abelian chiral gauge theory have been constructed based on Abelian bosonization. It is remarkable about these 2D lattice formulations that they reproduce the same gauge anomaly structure as the continuum theory, even at a finite lattice spacing. In this talk, we propose yet another lattice formulation based on the ``excision method'' introduced recently in Ref.~\cite{Abe:2023uan}. This approach respects the admissibility condition, which is a constraint on the smoothness of lattice field configurations; it usually prohibits magnetically charged objects, that is, vector-charged objects in fermion theories. We show that such objects can be defined in the excision method as a lattice defect called a ``hole,'' and discuss the selection rules for charged objects.