New conformal field theories by gauging electric and magnetic currents

TL;DR

This paper proposes a novel method to construct new conformal field theories with $U(1)$ gauge symmetry by gauging both electric and magnetic $U(1)$ symmetries, potentially overcoming previous no-go results.

Contribution

It introduces a new approach to generate conformal field theories by gauging electric and magnetic symmetries, suggesting the existence of fixed points in four-dimensional $U(1)$ gauge theories.

Findings

Potential existence of non-trivial RG fixed points for $U(1)$ gauge coupling.

Construction of new conformal field theories without $U(1) imes U(1)$ global symmetry.

Implications for CP-violation and $ heta$-parameter renormalization.

Abstract

Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ 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 $U(1)$ gauge symmetry by gauging $U(1) \times U(1)$ global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a non-trivial renormalization group fixed point for the $U(1)$ gauge coupling constant and it will be a non-trivial conformal field theory without the $U(1)\times U(1)$ global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the $\theta$-parameter is accompanied.