  Conformal perturbation theory is a powerful tool to describe the behavior of
statistical-mechanics models and quantum field theories in the vicinity of a
critical point. In the past few years, it has been extensively used to describe
two-dimensional models and recently has also been extended to three-dimensional
models. We show here that it can also be used to describe the behavior of
four-dimensional lattice gauge theories in the vicinity of a critical point. As
an example, we discuss the two-point correlator of Polyakov loops close to the
thermal deconfinement transition of $SU(2)$ Yang-Mills theory. We show that the
short-distance behavior of this correlation function (and, thus, of the
interquark potential) is described very well by conformal perturbation theory.
This method is expected to work with a similarly high accuracy for all critical
points in the same universality class, including, in particular, the critical
endpoint in the QCD phase diagram.
