Descrizione in teoria di stringa dei correlatori di loop di Polyakov in uno spazio compattificato

It is well known that finite temperature QCD undergoes a phase transition be- tween confined and deconfined states. While the deconfined phase has been widely understood by the use of perturbative theories, the confined one is still under inves- tigation. A possible mechanism to explain confinement for a mesonic boundstate is the formation of a strong chromoelectric flux tube between the two quarks. This ef- fect can be studied analytically on the lattice through the analysis of a correlator of two Polyakov loops and can be represented, at large inter-quark distance, by a low energy Effective String Theory (EST). In the lattice picture, the Polyakov loops represent a pair of static quark and anti-quark. On the other hand, in the string picture, they are identified by two D0- branes obtained from the one loop vacuum diagram of the string, embedded in a space with the time direction compactified on a circle. Thus, the string draws a cylindrical worldsheet in the embedding space. The aim of this work is to study the effect on the string energy and states spectra of the compactification of a further transverse spatial dimension. This introduces a new length scale (i.e. the length of the compact dimension) which interplays with the pre-existing ones and settles the energies of the excitations. In addition, since the endpoints are fixed on the Polyakov loops, the string can wind around the new compact dimension, giving rise to a new quantic winding number.