The Casimir Energy in QCD: from non-perturbative vacuum to flux tube

I will investigate the QCD flux tube (confining string) between 2 static color charges (q and qbar) in terms of the Casimir force. The latter is a famous consequence of the non-emptiness of the quantum vacuum, with experimental verification in the QED case: 2 parallel (uncharged) plates undergo a net force due to the quantized electromagnetic field. In the case of QCD, which handles the strong interaction, the Casimir force is far less understood. The working hypothesis is that in the non-perturbative QCD vacuum, the Casimir effect favors the formation of an energetically stable 3D cylinder-shape between the boundary charges, embedded in the normal vacuum. Inspiration is drawn from the 'old' nucleon bag models. I will develop new methodology for non-Abelian gauge theories in (2+1)-dimensions, where the cylinder becomes a rectangle, making the computations somewhat easier. A first novelty in the approach will come from QCD vacuum effects encoded by a non-perturbative path integration scheme. The associated mass gap equation will have an interesting interplay with the geometric cylinder/rectangle parameters and thence can drive the tube formation. A second novelty will be the inclusion of boundary charges in a gauge invariant fashion via non-local, dressed field configurations. Finally, I will probe the melting properties of the tube if the temperature is switched on, in search of a fresh perspective on the deconfinement phase transition.