Stability properties of an Abelianized chromoelectric flux tube

The quantum fluctuations about a uniform chromoelectric field confined to a cylindrical region are computed. The effective Lagrangian determined from this procedure yields the following interesting results. (1) The chromoelectric flux contained in this region must be less than a calculable critical value to preclude the existence of unstable fluctuation modes which would render the calculation ill-defined. (2) At a flux below this critical value, the fluctuations tend to make it energetically favorable for the flux tube to collapse upon itself. (3) Making analogies between this chromoelectric flux-tube model and physical hadronic strings, we estimate that the string of flux in a physical QQ-bar hadronic system is well within the region of stability. However, if the quark charges are increased by a factor of roughly 3, the string would become unstable by the above mechanism. This is given as an argument against the existence of certain exotic quark states.