Large charge operators at large spin from relativistically rotating vortices

We study the ground states of CFTs with a global $U(1)$ symmetry on $\mathbb{R}\times S^2$ in the regime of large charge $Q$ and large angular momentum $J$, using large charge EFT. We find that in the range $Q \ll J \ll Q^2$, the ground state solution is a superfluid densely populated with vortices rotating at a constant angular velocity $\Omega$. This is a relativistic generalization of the known (non-relativistic) rigid rotation phase, which corresponds to the small $\Omega$ limit of our solution. In the regime $Q^{3/2}\ll J\ll Q^2$, our solution achieves lower energy than previously identified states. In this regime, most of the vortices move near the speed of light, and we obtain the chiral fluctuation modes propagating at the speed of light. Interestingly, we find that our ground state can be interpreted as a zero temperature charged normal fluid rotating at a constant angular velocity $\Omega$. We rederive this solution purely from the fluid dynamics. Based on the (already established) applicability of fluid description to large non-supersymmetric extremal AdS black holes, we find that the boundary stress tensor and $U(1)$ current of extremal AdS Kerr-Newman black hole align with those of our solution.