Higher-derivative four-dimensional sine–Gordon model

The phase structure of a higher-derivative sine–Gordon model in four dimensions is analyzed. It is shown that the inclusion of a relevant two-derivative term in the action significantly modifies some of the results obtained by neglecting this operator, and the final picture is substantially different from the one describing the phase diagram associated with the two-dimensional Berezinskii–Kosterlitz–Thouless (BKT) transition. The study is carried out with the help of the Renormalization Group (RG) flow equations, determined for a set of three parameters, and numerically solved both for a truncated series expansion approximation, and for the complete set of equations. In both cases, a continuous line of fixed points, terminating at a particular point presenting universal properties, is found, together with a manifold that separates two phases, roughly characterized by the sign of the coupling ${\tilde{z}}_k$ associated with this newly included operator. While the phase corresponding to ${\tilde{z}}_k>0$ shows some pathologies, the one with ${\tilde{z}}_k<0$ has a well-behaved infrared limit, where the system reduces to a Gaussian-like model. We also briefly comment about the possibility that our model could capture some of the qualitative features of the ultraviolet (UV) critical manifold of conformally reduced gravity.