Condensed Matter Seminar: Shu-Heng Shao

Anomalies and Charged Operators
We study implications of ‘t Hooft anomalies for the local operator spectrum in gapless phases described by 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.