New conformal field theories by gauging electric and magnetic currents

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.

arXiv comment12 pages, v2 some improvement

References in corpus (18)

• On Renormalization Group Flows in Four Dimensions
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• New N=2 Superconformal Field Theories in Four Dimensions
• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• Central charges of N=2 superconformal field theories in four dimensions
• On Scale and Conformal Invariance in Four Dimensions
• CP-violating CFT and trace anomaly
• Dirac Relation and Renormalization Group Equations for Electric and Magnetic Fine Structure Constants
• On the realization of impossible anomalies
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Anomaly Constraints on Monopoles and Dyons
• CP-violating super Weyl anomaly
• Spurious Poles in the Scattering of Electric and Magnetic Charges
• Construction of a Model of Monopolium and its Search via Multi-Photon Channels at LHC
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• Strong gauging or decoupling ghost matter
• Anomalous hydrodynamics with dyonic charge