Bounds on Abelian Currents in 4d CFTs

We study four-dimensional conformal field theories (CFTs) with an abelian $U(1)$ global symmetry using the conformal bootstrap approach. We obtain numerical bounds on the scaling dimensions of low-lying operators, the stress-tensor central charge, and a particular combination of the 't Hooft anomaly and the current central charge. Our analysis provides the first non-perturbative constraints on four-dimensional CFTs with conserved abelian currents and establishes a framework that can be extended to theories with non-abelian global symmetries.