Bounds on Abelian Currents in 4d CFTs

TL;DR

This paper employs the conformal bootstrap method to derive non-perturbative bounds on key parameters of 4d CFTs with abelian symmetries, advancing understanding of these theories' operator spectra and anomalies.

Contribution

It provides the first non-perturbative bounds on operator dimensions, central charges, and anomalies in 4d abelian CFTs, establishing a new analytical framework.

Findings

Numerical bounds on operator scaling dimensions

Constraints on stress-tensor central charge

Limits on 't Hooft anomaly and current central charge

Abstract

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.