Exact partition functions for the effective confining string in lattice gauge theories

An important open problem in the study of confining gauge theories is the study of the behaviour of the  quark-antiquark potential. The standard approach to this problem is to describe the flux tube joining the quark-antiquark pair using string theory inspired effective models. In this respect one of the most  succesfull effective description is represented by the  the Nambu-Goto string. As a matter of fact this model has a much wider range of applications  since it can be used to describe all the physical situations   dominated by the d.o.f. of fluctuating surfaces, like   fluid interfaces in statistical systems. In this talk, after a brief introduction to lattice gauge theories  and to the physics of the interquark potential we shall show that, by using standard covariant  quantization, it is possible to  integrate the NG partition function over the world-sheet, getting an exact expressions in dependence of  the geometry of the surface spanned by the string in target space. This expressions resums the perturbative  expansion of the functional integral approach in the "physical gauge" and compares very well to avaliable  MC data both for the interquark potential and for interfaces free energy  in the regime of sufficietly large sizes where the conformal anomaly for d < 26 has negligible  effects.