# Superfluids, vortices and spinning charged operators in 4d CFT

## TL;DR

This paper explores the inclusion of vortices in the superfluid effective field theory for 4D conformal field theories at large charge, analyzing their effects on operator dimensions and correlators across various regimes.

## Contribution

It introduces vortices into the superfluid EFT framework for 4D CFTs and computes their impact on operator scaling dimensions and correlators, extending understanding of large charge sectors.

## Key findings

- Vortices correspond to charged operators with large spin.
- Scaling dimensions vary across phonons, vortex rings, Kelvin waves, and vortex crystals.
- Results are applicable in arbitrary spacetime dimensions.

## Abstract

We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions.