Effective string theory description of the interface free energy

We compare the predictions of the Nambu-Goto effective string model with a set of high precision Monte Carlo results for interfaces with periodic boundary conditions in the 3D Ising model. We compute the free energy in the covariant gauge exactly, up to the inclusion of the Liouville mode. The perturbative expansion of this result agrees both with the result evaluated several years ago by Dietz and Filk in the physical gauge and with a recent calculation with the Polchinski-Strominger action. We also derive the effective string spectrum which, because of the different boundary conditions, is very different from the well known one of Arvis. Taking into proper account the effective string corrections and exploiting some technical improvements in the simulations we obtain precise estimate of the amplitude ratios T_c/\sqrt{sigma}, m_{0++}/\sqrt{\sigma} and sigma xi_{2nd}^2. We also discuss the behaviour of the effective string free energy in the dimensional reduction limit (i.e., near the deconfinement transition of the dual 3d gauge Ising model) and its relationship with the 2d Ising model interfaces