Speaker
Description
Two-dimensional Abelian chiral gauge theories provide a useful setting for studying the interplay between gauge invariance, locality, and anomalies on the lattice. In this talk, I will discuss a lattice formulation of 2D $U(1)$ chiral gauge theory based on bosonization, with particular emphasis on magnetically charged vertex operators.
In the bosonized description, charged fermionic operators are represented by vertex operators of scalar fields. The corresponding dual vertex operators carry magnetic charge and therefore require a careful lattice definition. I will explain how such operators can be realized geometrically by excising small regions from the lattice, so that an operator insertion is represented as a hole. This construction gives a concrete way to define charged operators while preserving exact gauge invariance for anomaly-free fermion contents. I will also discuss how anomaly cancellation is reflected in the bosonized lattice theory and what this viewpoint suggests for lattice approaches to chiral gauge theories and anomalies.