# Bosonization with a background $U(1)$ gauge field

## TL;DR

This paper introduces a new bosonization method for Dirac fermions coupled with a $U(1)$ gauge field that maintains gauge invariance, anomaly matching, and operator correspondence, resolving previous issues and accurately capturing critical lattice model properties.

## Contribution

The work presents a novel bosonization framework for Dirac fermions with background gauge fields that satisfies key physical consistency conditions and improves upon previous models.

## Key findings

- Resolves the Dirac-mass condensation paradox.
- Accurately captures conformal dimensions and anomalies of lattice models.
- Establishes equivalence of fermionic flux and bosonic background charge insertion.

## Abstract

Bosonization is one of the most significant frameworks to analyze fermionic systems. In this work, we propose a new bosonization of Dirac fermion coupled with $U(1)$ background gauge field consistent with gauge invariance, global chiral anomaly matching and fermion-boson operator correspondence, either of which is not satisfied by previously developed bosonizations. The bilinear Dirac-mass term condensation paradox and its generalized form are resolved by our bosonization. This new bosonization approach to interacting systems also correctly captures the conformal characters of a significant class of critical lattice models, such as conformal dimensions and conformal anomaly of XXZ spin chain with twisted boundary condition. Our work clarifies the equivalence of fermionic flux insertion and bosonic background charge insertion for two-dimensional conformal field theory.