Il potenziale quark-antiquark e il Bethe Ansatz termodinamico

The study of the relation between the quark-antiquark confining potential and integrability has given, in the last years, interesting results through the use of thermodynamic Bethe Ansatz (TBA) method. The spectrum of low-lying states of a D-dimensional confining gauge theory is described, at large separations of a static pair of sources, by an effective string theory. In the far infrared limit, in the static gauge, it flows to a two-dimensional massless free-field theory. The first allowed correction to the Nambu-Goto (NG) action is quantum integrable, thus the energy spectrum can be found throught the TBA. This requires the use of the massless TBA, introduced by Zamolodchikov for the flows between tricritical and critical Ising model. In order to ensure the Lorentz invariance of the theory, the open-closed string duality must be satisfied: we obtain Luscher's constraints for NG using boundary TBA and the g-function. A generalization of TBA approach is the single non-linear integral equation (NLIE) proposed by Destri and de Vega: this allows to study further features of integrable models that are useful to the NG spectrum investigation as well.