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. [1]. 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.