Large charge operators at large spin from relativistically rotating vortices

TL;DR

This paper investigates large charge and angular momentum states in conformal field theories with a U(1) symmetry, revealing a superfluid vortex structure at high spin and connecting it to extremal black hole physics.

Contribution

It introduces a relativistic vortex superfluid solution for large charge and spin in CFTs, extending known non-relativistic rotation phases and linking to black hole boundary data.

Findings

Ground state is a rotating superfluid with vortices at relativistic speeds.

Most vortices move near the speed of light in high angular momentum regime.

Boundary stress tensor matches extremal Kerr-Newman black hole predictions.

Abstract

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.