# The bosonized version of the Schwinger model in four dimensions: a blueprint for confinement?

## TL;DR

This paper explores a 4D extension of the Schwinger model, demonstrating that it exhibits confinement through a linear potential, and relates it to topological models similar to QCD, providing insights into non-perturbative phenomena.

## Contribution

It introduces a 4D bosonized Schwinger model showing confinement and connects it to $B $ models and topological sectors of QCD.

## Key findings

- The static potential in the 4D model contains a linear confining term.
- The model appears as a version of $B $ models under dualization.
- The model involves mixing between a $U(1)$ potential and an Abelian 3-form field.

## Abstract

For a $(3+1)$-dimensional generalization of the Schwinger model, we compute the interaction energy between two test charges. The result shows that the static potential profile contains a linear term leading to the confinement of probe charges, exactly as in the original model in two dimensions. We further show that the same 4-dimensional model also appears as one version of the $ B \wedge F$ models in $(3+1)$ dimensions under dualization of Stueckelberg-like massive gauge theories. Interestingly, this particular model is characterized by the mixing between a $U(1)$ potential and an Abelian $3$-form field of the type that appears in the topological sector of QCD.