Conformal Bootstrap At Large Charge

Understand

We consider unitary CFTs with continuous global symmetries in $d>2$.

• We consider a state created by the lightest operator of large charge $Q \gg 1$ and analyze the correlator of two light charged operators in this state.
• We assume that the correlator admits a well-defined large $Q$ expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists.
• We find that the crossing equations admit a consistent truncation, where only a finite number $N$ of Regge trajectories contribute to the correlator at leading nontrivial order.