New conformal field theories by gauging electric and magnetic currents

Abstract

Old folklore says that there is no nontrivial renormalization group fixed point with [Formula: see text] gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially infinitely many) novel types of field theories with [Formula: see text] gauge symmetry by gauging [Formula: see text] global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a nontrivial renormalization group fixed point for the [Formula: see text] gauge coupling constant and it will be a nontrivial conformal field theory without the [Formula: see text] global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the [Formula: see text]-parameter is accompanied.