Conformal perturbation is a powerful tool to describe the behavior of statistical mechanics models and quantum field theories in the vicinity of a critical point. It was widely used in the past to describe two dimensional models and has been recently extended, thanks to the remarkable results of the bootstrap approach, also to three dimensional models. We show here that it can be also used to describe the behavior of (3+1) lattice gauge theories in the vicinity of a critical point. We discuss as an example the behavior of Polyakov loop correlators in the vicinity of the deconfinement transition of the (3+1) SU(2) Lattice Gauge Theory. We show that the short distance behavior of the correlator (and thus of the interquark potential) is precisely described by conformal perturbation theory and that this result can be used to constrain the effective string description of the theory in the confining phase.