Large charge operators at large spin from relativistically rotating vortices (2501.07198v2)

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.

• The paper establishes that a superfluid ground state emerges in CFT at large charge and spin, characterized by vortices rotating at nearly the speed of light.
• It employs a large charge effective field theory to derive energy-charge scaling laws, notably Δ² = J² + c₁²Q³, affirming robust quantum dynamics.
• The findings bridge vortex dynamics in superfluids with the holographic features of extremal AdS black holes, offering fresh insights into quantum gravity.

Large Charge Operators at Large Spin from Relativistically Rotating Vortices

The paper "Large charge operators at large spin from relativistically rotating vortices," examines the structure of ground states in conformal field theories (CFTs) with a global $U(1)$ symmetry on $\mathbb{R}\times S^2$. The analysis is conducted in the regime of large charge $Q$ and angular momentum $J$ using a Large Charge Effective Field Theory (EFT) framework. The aim is to determine the ground state characteristics characterized by these extensive quantum numbers, focusing on the energy spectrum and the fundamental properties of the system.

The authors identify distinct regimes for the charge and spin and analyze the ground state configurations. They establish that for $Q \ll J \ll Q^2$, the ground state forms a superfluid permeated by a high density of vortices, which rotate at a constant angular velocity $\Omega$. The solution presented is a relativistic extension of the non-relativistic rigid rotation phase, with vortices rotating near the speed of light in the regime $Q^{3/2}\ll J\ll Q^2$. As such, the identified ground state achieves lower energy than previously recognized states, suggesting an interpretation akin to a zero-temperature charged normal fluid.

Re-examining the solution from fluid dynamics principles, the paper finds alignment between the fluid description and the characteristics of large non-supersymmetric extremal AdS Kerr-Newman black holes. Notably, the correspondence between the dynamics of the superfluid vortices and the black hole aligns the boundary stress tensor and $U(1)$ current of the black hole with that of the ground state, hinting at broader applicability of fluid dynamics concepts to gravitational settings.

The paper also explores the energy-charge relationship within the system, deducing a significant formula for the large charge expansion in this charge-spin regime, namely: $\Delta^2 = J^2 + c_1^2 Q^3 + \cdots$ where subleading terms, governed by the EFT's validity, indicate that the relation holds over a wide range where $Q \ll J \ll Q^2$.

In deriving this result, the authors focus on an effective description of vortices, treating $\xi_\mu$ — the Goldstone boson's derivative — as an independent variable that captures both the vortex density and vortex flow. This approach allows a more robust mathematical framework for addressing fluctuations and emergent modes, revealing chiral fluctuations which propagate at light speed and signal the approach to the Regge limit as $J \sim Q^2$.

The investigation also establishes the interface between superfluid ground states and holographic theories of extremal black holes, contributing to the broader discussion of AdS/CFT correspondence and its implications for understanding quantum gravity. Differences between superfluid and fluid mechanics in this context underscore the nuances present when dropping to zero temperatures, where quantum mechanical features obscure classical fluid descriptions.

Looking forward, the implications of this work suggest increased exploration into the spontaneous generation of vortex-rich states and the manner in which they might parallel more complex gravitational dynamics hinted at by AdS/EFT correspondences. Future research could broaden these insights to non-Abelian symmetries or higher dimensions, deepening our grasp of CFT dynamics and their cosmological analogs. This paper lays the foundation for understanding the rich interplays between field theories and gravitational solutions, potentially unlocking novel theoretical tools or methods applicable across theoretical physics.