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.
Highlights
Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions
This is a consequence of the state/operator correspondence [11, 12], which relates states in radial quantization to local operators with the same quantum numbers
We study the predictions of the vortex effective field theory (EFT) for four dimensional CFTs
Summary
Let us first set our conventions for the four dimensional rotation group SO(4). Spinning operators in four dimensions are classified in representations labelled by two positive halfinteger quantum numbers (J, J). The main prediction of the superfluid EFT is the scaling dimension of the lightest scalar operator of charge Q in the spectrum It is given by [13]. For Q J12 ≤ J34 Q4/3 the superfluid arranges in a vortex lattice as in (1.6); the scaling dimension of the corresponding operator is. These results apply to CFTs whose large charge sector can be described as a superfluid and which admit vortices. In 5 we show how to make predictions for correlators involving a current insertion between two vortex states and in 6 we briefly comment on how the results (1.4) and (1.6) change in generic spacetime dimensions. For fixed η different from 0 and π/2, ξ and φ describe an S1 × S1 submanifold
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