Identifying Large Charge operators

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum spinning large charge operators. For sufficiently low spin these correspond to phonon excitations state. We discuss organization states into conformal multiplets and form corresponding composite operators in free field theory limit. latter entails mapping, built order-by-order inverse $n^{-1}$, between Fock space vacuum fluctuations limitations method, find that description breaks down for spins order $n^{1/2}$ while computation observables is valid up $n$. Finally, apply method compute some 3-point 4-point functions, analyze block decomposition with our knowledge operator spectrum.