On the behaviour of the interquark potential in the vicinity of the deconfinement transition

In the vicinity of the deconfinement transition the behaviour of the interquark potential can be precisely predicted using the Effective String Theory (EST). If the transition is continuous we can combine EST results with a conformal perturbation analysis and reach the degree of precision needed to detect the corrections beyond the Nambu-Goto approximation in the EST. We discuss in detail this issue in the case of the deconfinement transition of the SU(2) gauge theory in $(2+1)$ dimensions (which belongs to the same universality class of the 2d Ising model) by means of an extensive set of high precision simulations. We show that the Polyakov loops correlator of the SU(2) model is precisely described by the spin-spin correlator of the 2d Ising model not only at the critical point, but also down to temperatures of the order of $0.8 T_c$. Thanks to the exact integrability of the Ising model we can extend the comparison in the whole range of Polyakov loop separations, even beyond the conformal perturbation regime. We use these results to quantify the first EST correction beyond Nambu-Goto and show that it is compatible with the bounds imposed by a bootstrap analysis of EST. This correction encodes important physical information and may shed light on the nature of the flux tube and of its EST description.