STRING FORMATION IN THE MODEL OF THE STOCHASTIC VACUUM AND CONSISTENCY WITH LOW ENERGY THEOREMS

We re-derive and discuss two low energy theorems which relate the potential of a static quark-antiquark pair with the total energy and action stored in the flux tube between the sources. In lattice QCD these relations are known as Michael's sum-rules, but we give an essential correction to one of them. Then we relate the low energy theorems to the virial theorem for a heavy quark-antiquark bound state. Finally we compare the results for the flux tube formation, which have been calculated in the model of the stochastic vacuum, with the low energy theorems and obtain consistency. From this we conclude that the model describes the non perturbative gluon dynamics of QCD at a renormalization scale, where the strong coupling constant is given by $\al_s = 0.57$.