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

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 ∧ 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