Isotropic Lifshitz scaling in four dimensions

The presence of isotropic Lifshitz points for a O(N)-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension d = 4, evidence for a continuous line of fixed points is found for the O(2) theory, and the observed structure presents clear similarities with the properties observed in the two-dimensional Berezinskii-Kosterlitz-Thouless phase.