Anomalies and Charged Operators
Abstract: We study implications of 't Hooft anomalies on the local operator spectrum in conformal field theory. Using the modular bootstrap, universal bounds on (1+1)-dimensional conformal field theories with an internal Z2 and U(1) global symmetry are derived. The bootstrap bounds depend dramatically on the ’t Hooft anomaly. In particular, there is a universal upper bound on the lightest charged operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. Finally, we comment on the more general anomalies that cannot be captured by TQFTs, a notion known as the "symmetry enforced gaplessness" in condensed matter physics.
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