Charged spinning operators in CFTs: from superfluids to Regge theory

In CFT, states with large quantum numbers often admit a simple universal description. Most famously, CFTs become approximately free in the large spin sector, with operators organized in Regge trajectories labeled by the twist. On the other hand, operators with large quantum numbers under the internal symmetries of the theory often admit an effective hydrodynamic description. In this talk, I will review these results and I will propose a series of EFT descriptions for operators with both large charge and large spin in 3d CFTs. The results smoothly interpolate between the hydrodynamic regime and the large spin Regge theory. Based on 1711.02108 with A. De la Fuente, A. Monin, D. Pirtskhalava, R. Rattazzi, and 2210.15694 with Z. Komargodski.